I would keep this pigeon and call it you're own there does not seem to be a contact that is reliable. If you know birds, as you seem to do..it is in good hands..
The bird sounds sick, do you have any antibiotics around to treat him for say 10 days.. can you post a picture of him and his droppings? how much is he eating? he may like to have a heating pad under the box to reserve his energy.Dang. Got up this morning to find it is much weaker. You have to hold the water dish right under its beak now because it's having trouble standing. It would be an awful shame for it to have survived 800+ miles and Gulf storms, but run out of fight just when it got rescued.
We bought commercial pigeon feed for a mourning dove nestling we rescued a while ago, so I think it's getting a good grain mix - I will take Hareloft's suggestion and add a little game bird feed on the side for extra protein, though.
If it doesn't recover well enough to fly home, I don't imagine shipping it - but I really would like to at least let its people know where it wound up. It's had an amazing journey, and it's a good-looking bird.