What about putting down a washable rug, with a latex backing, in the area he likes to go?

It sounds like you did save him. Dogs were not meant to go in their crates. A crate is suppose to be a substitute for a den (where it would have been in the wild), and no dog wants to go where he sleeps. I think it is cruel for those so called breeders to do this. Also, it makes it very hard to crate train a dog after the fact. FYI I prefer crate training a dog for potty purposes.
But back to your problem. Have you tried natures miracle on the carpet? He will continue to go in that same area as long as he can smell it, and even though you may think that it is clean, dogs have much better sniffers than we do. I would try the natures miracle and keep him away from that area until you have him trained to go in an area of your choice. I would start by retraining him with the crate method. If you are unfamiliar with the crate method, there are excellent intructions online. Just make sure that you use the smallest crate that he can fit in. He should be able to stand and turn around, but that's about it. Once he has gotten the hang of holding it for a couple of hours and relieving himself in the correct location, then you can start to expand his area. Slowly transition to a larger crate space and then into a confined area of a room, and onto a larger section of room, and so on.
If you follow the methods to a T, he will be trained in no time. And if he has an accident, then just reduce his space back 1 step and continue as before. But the main thing right now is to get rid of the urine smell.