First of all, welcome to TCS! Glad you found us, and hope we can help.
1) Many cats do not like to pee and poop in the same litter box. Have you considered getting a second litter box? This may be all you need to do.
2) Are you sure there's not a medical problem? It seems this problem has been going on for some time - but has the kitty had a vet visit? The only way cats have to tell us there's a medical problem is by pooping or peeing outside of the litter box - or changes in behavior (sometimes even just subtle ones). If your kitty hasn't seen a vet, make an appointment, get a sample of the poop, put it in the fridge, and bring it with you when you take kitty to the vet.
3) He may have worms. Again - this is something a vet should tell you. De-worming meds you can get at a pet store DO NOT WORK.
4) How long have you been putting him in the cat cage and how long has he been pooping in the litter box in there? "Retraining" is often a step taken to work with kitties that poop outside the litter box - and that involves doing just what you are - only not letting them out of the confined area until they're consistently using the litterbox to poop in. Then the idea is to allow kitty access to an entire room - and when kitty continues to poop in the litter box, access to the rest of the house.
Again - I think a second litter box may be all that's needed here.
Also, I don't know how frequently you scoop the litterbox, but some kittes are really fussy about clean litter boxes. Scooping both morning and evening, and totally emptying and bleaching the box once a month and filling it with entirely new litter may help. Do this for both boxes.
Ummm... let's see. I don't know what you've been using to clean up his poop, but you MUST use an enzyme cleaner. Regular cleaners or carpet cleaner will NOT do the trick. Nature's Miracle is one that is available at most pet stores or supermarkets. We've found that this product works even better: http://www.nokout.com
The area must be free of any smell to kitty (and they have FAR more sensitive noses than we do!). The only way to do this is with an enzyme cleaner - or kitty will keep going in the same place (or near it). If it smells like a bathroom to kitty, it is one.
You can purchase Oil of Olbas at a health food store. When you have soaked the area with the enzyme cleaner and blotted it after the 10 minutes soak, lie aluminum foil over the area. Kitty will not want to poop on aluminum foil. The soak a tea bag, put a few drops of Oil of Olbas on it, and set it on a small plate on the aluminum foil. Kitties do not like Oil of Olbas, and will avoid the smell - so don't do it if it's near the litter box. Just put the aluminum foil down until the area (if carpeted) you soaked is completely dry. And it may not say it on the directions - but with the enzyme cleaner if the area is carpet - you must soak it down to the floorboards, so it may take a day or two to dry completely.
You may want to read this thread: Inappropriate Poop Problems Answered
Please feel free to post with any more questions!
....and thank you for rescuing this kitty!