While true that you can use any lender you like, you could try Lending Tree and see what you come up with. Or shop a broker for the best rate. I've considered doing the same thing on one of my paid off rentals, but I think I'd rather 10-31 exchange it and get three similar properties with leverage. It's not in the best location, on a busyish street.
Right now I'm still thinking about it but just sitting on it until I know for sure it's the right thing to do. The house has gone up in value, more than doubling in the past five years. Rents are great, but my cash on cash return is so low now that I would be better off putting it into the market. Either that or 10-31 it and buy three leveraged properties with the money in the same area but not on a busy street. That would give me high returns initially again, but as the price rises and the mortgage is paid off, my returns will drop drastically once again.