Way back in what seems like another era (there wasn't even a patriot league then) I ended up at a current patriot league school through running and some good luck. Looking back I probably owe 99% of my career and life success to the education, values and opportunities I acquired there. This puts me squarely in the camp that it really does make a difference where one goes to college. If parents and student choose a state school over the best academic opportunity to save $200 to $250k, there should be a lot of thought put into how you will get the same outcome after 4 years. If financial aid makes both options cost about the same, then it's pretty clear to go for the best choice.
Over the past few years I have helped some very bright low income kids with college apps. Your daughter will qualify as a single parent child. Income under $60k per year guarantees basically a full ride just based on need to most of the top schools mentioned here. Under $100k per year can even work at some of the schools, and will for sure at least get 2/3 aid. When you file the aid forms, there is a special form for "no contact with parent", where you need to describe the whereabouts - can be unknown, and the situation as to why they are not in the child's life. This needs to be signed off by 2 people who know the child, and notarized.
While there will be no (or highly doubtful) scholarship money, the commitment to run and input to the admissions department, can really help the student get in to the college. You need to contact the coach and tell them that you are applying, as well as include the commitment to running in the application materials. As you probably know from your football, there might not be a scholarship, but the GPA and test scores needed to get into the school can be much lower for athletes.
You already have a lot of good info here on schools - I would have you look at the top D3 schools. The NESCAC schools in New England, Hopkins, Haverford, Dickinson Midwest Wash U, Grinell, Carleton, Mcalaster - West Pomona, Claremont, Scripps, Occidental, Reed. In D3 for an 18 minute lady, one is part of the school team, has a structure that is clear to understand ie. league meet, regionals, D3 nationals and of course the opportunity to train seriously and improve, but without the pressure of being the "worst one on the team" that can come at a D1 program. At most of the D3 schools, all the walk ons are on the team.
A great place to learn about how this whole financial aid process works is Questbridge.org which helps to match up low income kids with the financial aid available at top schools. 99% of the best schools (including Rice) are in this program and the information available there can really help to understand how the whole process works.
Good luck! Will be interesting to see the SAT/ACT scores, as without grades and scores these schools can be too much of a reach.