Aw, the pics aren't showing for me...
Kitty pee issues are awful, I agree. I've lost at least 2, maybe 3, comforters, and an assortment of clothing, bags, etc. to kitty pee.
While I can see why you think this might be behavioral, peeing out of the litterbox is a very common sign of a urinary tract infection, which can be brought on by stress. It's possible that Sweet P's arrival brought one on, so I'd bring Bizzle in for a vet visit to rule out any possible medical reasons. If it is a UTI, antibiotics will clear it up.
I'd also keep him inside so that you can monitor his litterbox habits. I totally get that having him inside when he's peeing out of the box is frustrating, but it will be harder to figure out what's going on if you can't keep an eye on what's going on, especially if it is a behavioral issue. For example, is he consistently peeing out of the box, or is he using it sometimes, but not always? If he is using it sometimes, is there one he prefers? Where is Sweet P when he's using/not using the box? Also, is he pooping in the box, just not peeing in it?
About the enzyme cleaner - do allow whatever you've completely soaked to dry completely before washing. I also discovered that Nature's Miracle has a laundry additive. I've used it after soaking/drying stuff. Not sure it's necessary, but psychologically it makes me feel better.