I am going to respond only for Bowdoin. My guess is that you would be an attractive candidate. While NESCAC is strong in many sports, football isn’t one of them, so you might fit into the program with less experience. They also value kids who can fill different roles on campus, and of course are also strong students. It would help enormously to have coach support, and if you do, you will need to apply ED. This puts you late in the process. But here’s the rub – it’s going to be over budget.
My guess is that most D3 schools would welcome you as a walk on, so keep in touch with coaches and share film as you get it. It’s going to be hard to get coach support for admissions with your timeline (because the quid pro quo for that support is ED) but you will want to be on their radar if you want to walk on. Because of cost, you want to consider the D3 schools that have merit. Folks have mentioned some of them upthread, but you might want to look at Union, Denison, Grinnell, Muhlenberg, Dickinson, Gettysburg to name a few.
With the big state schools, I would guess you are going to have to get in on your own and then try to walk on.
As mentioned, you could do a PG year at a prep school with a decent football program (Exeter, Lawrenceville, Taft, Canterbury are a few that come to mind), but that will cost the same as a year of college. It would, however, get you more experience and a chance to approach recruiting a bit differently.