Critters will get into straw bales for sure, regardless. They’ll chew on rigid foam too. Is your floor insulated? Do you have enough room under the floor to do anything?
I helped a friend insulate a floor in one of his outbuildings. (Man Cave) Kinda the same scenario (on piers with just enough room to get under it) It has 2×6’s so we used R-19 fiberglass between the floor joists. (2′ on center) Stapled it in and covered the whole belly with vapor guard. Used 1/2 inch squares by 2′ wide rat screen and covered the whole works, using furring strips and deck screws on the seams at each floor joist and on the edges along the outside parameter..
Once we got started, it went in fast and was quite easy. Just make sure you start the rat screen straight..
BTW.. Howdy, neighbor! I’m in East Central Ohio and been off grid since ’89..