For a "very remote" area, you're not far from some animal shelters, even without driving an hour to Tampa:
3195 Dundee Rd, Winter Haven, FL 33881
5850 Brannen Rd S, Lakeland, FL 33813
Won't be a high priority for them, but never hurts to ask for local advice. I think I'd just taper its food and let it survive on its own, but if there's anybody out there looking to adopt escaped pet pigeons, the SPCA is your best bet for finding such a person.