When cleaning up cat pee, you need to use an enzymatic cleaner. Period. Anything else is not going to work, and may actually make it worse (like you've noted... it can actually bring out the cat pee smell). Nature's miracle is one such, but there are many others, and some are made to work with a rug cleaner. A black light is also really useful. I'd lay off the boiling water, vinegar etc.
As far as preventing this behavior in the future, from what you've said it sure sounds like he's not accepting the litterbox that you've selected for him. Whether it be the location, the size of the box, the fact that it's covered, the litter itself, or the fact that there is only one of them, something is not clicking with him. And I think you're being a little too stubborn about it.
Jackson Galaxy has approached cases like this in a very cat-centric way. Rather than trying to guess, he'll tell clients to put down lots of boxes, with various litters and at various locations, and then you learn what he'll use, then you can start removing boxes. Some cats like to pee in one box, and poo in another, so think in terms of 2 boxes minimum, and most cats prefer boxes that are "open" rather than hooded. Some cats are really "control freaks" about litterboxes, so something like changing a location will trigger them to reject a litterbox. Jackson talked about how his cat preferred his litterbox to be in an inconvenient location (in the middle of a room) but in order to relocate it, he had to do it over a period of time, moving the box inches a day. Any more than that, would cause it to be rejected.
The other thing is that I'm guessing he must be a pretty huge cat (since he's part Savannah?). He may need a box bigger than any commercial box that you can buy in a pet store. Even for large pure-bengal males, I've heard a lot of members say that they had to improvise and create their own boxes to find something that would work.
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