Here's the more in-depth reasoning.
Regional and season results I'm using, tell me if there's a mistake or a meet I missed:
northeast = ['iona','columbia','syracuse','dartmouth','providence','harvard','cornell','yale'],
midatlantic = ['georgetown','villanova','princeton','american','penn state'],
southeast = ['virginia','eastern kentucky','nc state','virginia tech','duke','george mason','liberty','william and mary','wake forest'],
south = ['florida state','georgia','florida','georgia tech','mississippi state','chattanooga','east tennessee state','tennessee'],
southcentral = ['texas','arkansas','texas a&m','mcneese state','stephen f austin','rice','lamar'],
greatlakes = ['wisconsin','michigan','indiana','michigan state','notre dame','miami ohio','purdue','ohio state'],
midwest = ['oklahoma state','oklahoma','tulsa','illinois','missouri','kansas','minnesota','iowa state','southern illinois'],
mountain = ['northern arizona','byu','colorado','new mexico','weber state','air force','utah valley'],
west = ['stanford','portland','ucla','oregon','washington','arizona state','washington state','cal poly'],
rimrock = ['kansas','indiana','air force','texas tech','rice','new mexico state','nebraska'],
greaterlouisvilleclassic = ['iona','columbia','georgia','missouri','texas','louisville','arizona','michigan state','grand valley state','penn state','colorado state','kentucky','auburn'],
pac12preview = ['northern arizona','ucla','arizona state','cal poly','sacramento state'],
panoramafarms = ['oklahoma','arkansas','virginia','michigan','duke','california','kentucky','norfolk state'],
notredameinvite = ['tulsa','princeton','notre dame','florida state','eastern kentucky','new mexico','texas a&m','washington state','mcneese state','nc state','north carolina','eastern michigan','ohio state','illinois','indiana state','butler','navy'],
paulshort = ['villanova','william and mary','georgetown','dartmouth','providence','cornell','yale','lehigh','tennessee'],
cowboyjamboree = ['oklahoma state','utep'],
louisvilleclassic = ['iona','columbia','georgia','missouri','texas','louisville','arizona','michigan state'],
roygriak = ['minnesota','iowa state','weber state'],
dellinger = ['byu','oregon','southern utah','washington','gonzaga'],
wisconsininvite = ['stanford','iona','oklahoma','texas','arkansas','columbia','michigan','new mexico','eastern kentucky','ucla','syracuse','portland','northern arizona','princeton','indiana','iowa state','wisconsin','georgia','texas a&m','kansas','arizona state','washington','minnesota','illinois','arizona','notre dame','virginia','harvard','north carolina','cal poly','missouri','dartmouth','colorado state','nc state','michigan state','california','purdue','providence','ohio state','yale','penn state'],
chilepepper = ['oklahoma state','texas tech'],
prenats = ['colorado','byu','oregon','florida state','duke','virginia tech','tulsa','villanova','georgetown','eastern michigan','florida','louisville','boise state','william and mary','butler','mcneese state','air force','lamar','utep'],
mountainwest = ['new mexico','air force','colorado state'],
bigeast = ['syracuse','georgetown','notre dame','providence','villanova','louisville','cincinatti','marquette'],
sec = ['arkansas','georgia','missouri','texas a&m','florida','kentucky','tennessee','auburn'],
pac12 = ['colorado','stanford','oregon','arizona state','ucla','washington','arizona','washington state','california'],
ivyleague = ['princeton','columbia','dartmouth','cornell','harvard','yale'],
big12 = ['oklahoma state','texas','oklahoma','kansas','iowa state','texas tech','baylor'],
acc = ['virginia tech','virginia','florida state','nc state','duke','north carolina'],
big10 = ['wisconsin','michigan','indiana','illinois','minnesota','penn state','michigan state','ohio state'],
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Output of the algorithm:
Automatically selected:
1: wisconsin is selected, has losses to (wisconsininvite) new mexico, ucla, syracuse, princeton, indiana, iowa state;
2: michigan is selected, has no losses to teams remaining
3: georgetown is selected, has losses to (bigeast) syracuse; (prenats) colorado, oregon, duke, virginia tech, tulsa; (paulshort) william and mary;
4: villanova is selected, has losses to (bigeast) syracuse, notre dame, providence; (prenats) colorado, oregon, duke, virginia tech, tulsa;
5: oklahoma state is selected, has no losses to teams remaining
6: oklahoma is selected, has no losses to teams remaining
7: northern arizona is selected, has losses to (wisconsininvite) new mexico, ucla, syracuse;
8: byu is selected, has losses to (prenats) colorado;
9: iona is selected, has no losses to teams remaining
10: columbia is selected, has losses to (ivyleague) princeton;
11: florida state is selected, has losses to (acc) virginia tech; (prenats) colorado, oregon; (notredameinvite) tulsa, princeton, notre dame;
12: georgia is selected, has losses to (wisconsininvite) new mexico, ucla, syracuse, princeton, indiana, iowa state;
13: texas is selected, has losses to (louisvilleclassic) missouri; (greaterlouisvilleclassic) missouri;
14: arkansas is selected, has no losses to teams remaining
15: virginia is selected, has losses to (acc) virginia tech; (wisconsininvite) new mexico, ucla, syracuse, princeton, indiana, iowa state, texas a&m, kansas, arizona state, washington, minnesota, illinois, arizona, notre dame;
16: eastern kentucky is selected, has losses to (wisconsininvite) new mexico; (notredameinvite) tulsa, princeton, notre dame;
17: stanford is selected, has losses to (pac12) colorado;
18: portland is selected, has losses to (wisconsininvite) new mexico, ucla, syracuse;
Teams under consideration: syracuse (7), new mexico (6), princeton (6), colorado (5), ucla (5), virginia tech (4), tulsa (4), oregon (3), indiana (3), texas a&m (1), illinois (1), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), florida (0), georgia tech (0),
Others with points: notre dame (4), iowa state (3), duke (2), missouri (2), washington (1), arizona state (1), minnesota (1), providence (1), kansas (1), william and mary (1), arizona (1),
19: syracuse is selected, has losses to (wisconsininvite) new mexico, ucla;
Teams under consideration: new mexico (7), ucla (6), princeton (6), colorado (5), virginia tech (4), tulsa (4), oregon (3), indiana (3), providence (1), texas a&m (1), illinois (1), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), florida (0), georgia tech (0),
Others with points: notre dame (4), iowa state (3), duke (2), missouri (2), washington (1), minnesota (1), arizona state (1), kansas (1), william and mary (1), arizona (1),
new mexico not selected with push (gets in later on their own)
ucla wins head-to-head tiebreaker over princeton (relevant meets: wisconsininvite)
20: ucla is selected, has losses to (wisconsininvite) new mexico; (pac12) colorado, oregon, arizona state;
Teams under consideration: colorado (6), princeton (6), oregon (4), virginia tech (4), tulsa (4), indiana (3), providence (1), texas a&m (1), washington (1), illinois (1), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), florida (0), georgia tech (0),
Others with points: new mexico (8), notre dame (4), iowa state (3), duke (2), arizona state (2), missouri (2), minnesota (1), kansas (1), william and mary (1), arizona (1),
no head-to-head tiebreaker for colorado and princeton (relevant meets: )
colorado wins common opponents over princeton (common opponents: duke, boise state, louisville, air force, northern arizona, washington, minnesota, iona, texas a&m, north carolina, washington state, navy, columbia, portland, iowa state, villanova, cornell, oklahoma, byu, colorado state, ucla, arizona state, illinois, providence, eastern michigan, arkansas, michigan state, ohio state, indiana, mcneese state, texas, georgetown, lamar, arizona, wisconsin, tulsa, michigan, kansas, indiana state, virginia, oregon, butler, harvard, california, new mexico, eastern kentucky, dartmouth, utep, notre dame, syracuse, william and mary, georgia, stanford, virginia tech, purdue, florida, missouri, florida state, cal poly, yale, penn state, nc state)
21: colorado is selected, has no losses to teams remaining
Teams under consideration: new mexico (8), princeton (6), oregon (4), virginia tech (4), tulsa (4), indiana (3), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), florida (0), georgia tech (0),
Others with points: notre dame (4), iowa state (3), duke (2), arizona state (2), missouri (2), minnesota (1), kansas (1), william and mary (1), arizona (1),
22: new mexico is selected, has losses to (notredameinvite) tulsa, princeton, notre dame;
Teams under consideration: princeton (7), tulsa (5), oregon (4), virginia tech (4), indiana (3), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), florida (0), georgia tech (0),
Others with points: notre dame (5), iowa state (3), duke (2), arizona state (2), missouri (2), minnesota (1), kansas (1), william and mary (1), arizona (1),
23: princeton is selected, has losses to (notredameinvite) tulsa;
Teams under consideration: tulsa (6), oregon (4), virginia tech (4), indiana (3), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: notre dame (5), iowa state (3), duke (2), arizona state (2), missouri (2), minnesota (1), kansas (1), william and mary (1), arizona (1),
24: tulsa is selected, has losses to (prenats) oregon, duke, virginia tech;
Teams under consideration: oregon (5), virginia tech (5), indiana (3), missouri (2), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: notre dame (5), duke (3), iowa state (3), arizona state (2), minnesota (1), kansas (1), william and mary (1), arizona (1),
oregon wins head-to-head tiebreaker over virginia tech (relevant meets: prenats)
25: oregon is selected, has no losses to teams remaining
Teams under consideration: virginia tech (5), indiana (3), arizona state (2), missouri (2), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), nc state (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: notre dame (5), duke (3), iowa state (3), minnesota (1), kansas (1), william and mary (1), arizona (1),
26: nc state is selected, gives no points (pushed in)
27: virginia tech is selected, has losses to (prenats) duke;
Teams under consideration: duke (4), indiana (3), arizona state (2), missouri (2), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), george mason (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: notre dame (5), iowa state (3), minnesota (1), kansas (1), william and mary (1), arizona (1),
28: duke is selected, has no losses to teams remaining
Teams under consideration: indiana (3), arizona state (2), missouri (2), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), george mason (0), liberty (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: notre dame (5), iowa state (3), minnesota (1), kansas (1), william and mary (1), arizona (1),
29: indiana is selected, has losses to (rimrock) kansas;
Teams under consideration: notre dame (5), arizona state (2), missouri (2), providence (1), texas a&m (1), washington (1), illinois (1), weber state (0), air force (0), dartmouth (0), mcneese state (0), george mason (0), liberty (0), michigan state (0), american (0), penn state (0), florida (0), georgia tech (0),
Others with points: iowa state (3), kansas (2), minnesota (1), william and mary (1), arizona (1),
30: michigan state is selected, gives no points (pushed in)
31: notre dame is selected, has losses to (wisconsininvite) iowa state, texas a&m, kansas, arizona state, washington, minnesota, illinois, arizona;