There are plenty of very very bad D1 programs who will let you walk on with those times. I'm familiar with NC. I'm sure most states in America have a few schools on the low end who need to fill out their rosters.
I've sent athletes to UNCW, UNCG, ECU, Western Carolina, UNC-Charlotte all D1 schools with times around your cross country times in the last decade to walk on.
I've even sent 16:30 kids to schools like Appalachian State who got to try out and made the team but they worked their butts off over the summer for that chance. 16:30 want get you recruited there but they might let you try out.
You are correct your track times might make them rethink letting you walk on. If you get down to 4:40 and 10 flat you can almost guarantee you will be able to walk on to some D1 school if you look around.
Many low end D1 schools will take a 16:30 athlete to round out their roster but if you don't improve they will cut you and fill that spot again with someone else the next year.
The best way to find a school that will take a 16:30 guy is to look at the XC regional results and either look for teams that didn't send a team to regionals or a team that finished in the bottom 5. Those teams will jump on 16:30 athletes as long as they feel the athlete can handle the academics.