Can you clear out the room completely and use a carpet cleaner on it? There are ones you can rent (or if you have a friend or family member who would let you borrow theirs?) and you put a cleaning solution in with water and it does a very, very thorough job of cleaning and deodorizing. Since you’re also dealing with previous rabbit stains, that might be encouraging him to mark in that area even more. It does take about a day for the carpet to completely dry out, so he’d have to be somewhere else for about 24 hours. Once you got all the heavy stuff cleaned up, it would be much easier to just spot clean here and there if necessary.
We usually carpet clean in our house about twice a year. Since we do it so infrequently, we can’t justify buying or storing one in our tiny house, so my parents are kind enough to let us use theirs. At first glance, our carpet looks very clean (I vacuum constantly and we don’t wear shoes in the house!) but when it comes time to dump out the dirty water, it’s dark brown. Kind of gross to think you’re walking on that every day! Carpeting just takes a beating, even when treated well!