Agree with the above. You say you CANNOT lose them but it sounds like you might not have a choice. You're lucky they haven't been sold already as it is! Your barn owner is quite honestly a nicer person than I am. over 2,000 in back board is a LOT. More than just a month or two. And if I was boarding horses I would not allow that. You obviously can't afford them- and their care is suffering because of it (their hooves are so bad they're CURLED?). You need to think about them, not yourself. Where are you going to come up with the money to pay the backboard, the future board, AND the care they so desperately need? It's quite honestly a bit selfish to keep them in my opinion when you know you can't take care of them. What would you do if one needed a vet?
I'm sorry, but I agree with the sentiment that you need to sell. Not paying and moving your horses out just because you don't have a contract and don't have the money to follow the verbal contract is a nasty thing to do, and you don't want to be THAT person to run away because of problems you can't solve.