Hi Tara, I can totally sympathize with your predicament!! It can be a frustrating thing for a cat owner, because there are so many reasons why a cat may not be using the box. I know I posted this somewhere else before, but I'll go ahead and give you an overview on what we're doing with our "troublesome boy"!! LOL LOL
It sounds like you may be in a very similar situation as we are with our Scooter. My husband (boyfriend at the time this all happened) got his cat Scooter declawed and neutered at probably a little over 6 months of age. Later we noticed that he had started going to the bathroom on the carpet. Mostly at the baseboards around the room. Soooo...of course I go to the "drawing board" so to speak to see if we can solve the problem. First thing is to always rule out any kind of change that may have occurred. It could me anything from adding a new pet, to moving the food bowl to changing the litter or food. Once that kind of stuff is ruled out, rule out health problems next. UTI is a common thing in males cats, unfortunately.
Then I started doing a little research, and what I found was a bit disconcerting. There have been some studies by veterinarians that the declaw procedure can cause behavioral problems to develop, even up to years after the declaw procedure. The description of the behavior described my Scooter to a T (basically biting, eliminating outside the litter box, becoming a little more skittish etc). Unfortunately there's not much we can do at this point because we've tried everything. Sounds like you are on the right track with the cage. We can't trust poor Scooter out in the house whenever we are not home, so we put him in his "kitty playpen" that I got from Dr. Foster and Smith. So, now he's in this cage with his litter box food and water whenever no one is home to watch him. When we are home we let him out. The vet suggested us 2 different kinds of drugs that could help with the behavioral problem. One was valium and the other was Ovaban. We tried the Valium, but it really didn't help with the elimination problem. It helped with everything else though! LOL Aaron didn't want to do the ovaban because it has a rare, but serious side effect. Knowing our luck, our cat would be that one in 10000 or whatever that dies from it. Ovaban can cause a type of cancer...but it's very rare that they see that happen. But we just decided to try the valium. No harm there. You could talk with your vet about the possibility of a behavior problem and he might suggest you to try valium.
Our poor Scooter just recently recovered from a severe UTI as well! He's had several ocurrances, so finally our vet put us on a prescription diet that he has to be on for the rest of his life. It's a Hill's Science Diet prescription. You may want to check into that as well...so help a recurrance

Also,...boy am I babbling or what??LOL....it's so unfortunate about the carpet. I know that feeling!! Visit the Drs Foster and smith website(www.drsfostersmith.com). They have a product that I use for stains and such called stain away. You might want to give that a shot to see if it helps with the stains/smells in the carpet. Good luck and let us know how he's doing!!!