I really think it's behaviour with Gizzy, but I did notice in a previous post that you changed his litter a week ago to Sweat Scoop
. It could be the litter change has something to do with his peeing on the bed.
I had a funny thing happen recently with my cats---they both use one box which they've always preferred. I was using a clumping clay litter that was OK but a little dusty. My neighbour raved about World's Best (corn meal) cat litter and said her cat loved it and she did too as there was no dust. So I thought I'd give it a try. The cats accepted it without any fuss, though it did have a "corn" smell. I've been using it for almost a month but last week my girl used it OK but had no urge to cover up her pee clumps or poops. My boy was fine with it and covered up his stuff, but not hers. One day, she actually did her poop outside
the box. Then I noticed she meowed and fussed a bit before going into the box. So decided to go back to the clumping clay litter. I cleaned the box thoroughly to get rid of any corn smell, and as soon as I put the clay litter in, she got in pooped and covered it up. No problemo! That was on the weekend and she's continuing to cover everything up. Have no idea what it was that she didn't like about the Worlds Best corn meal litter, maybe the smell? because it was lighter in weight and a bit coarser than the clay litter? Who knows? But she wasn't completely happy with it, and that was her way of telling me she didn't like it.
Soooo, if Gizzy was doing well on the litter you used before you switched to Sweat Scoop, go back to it and see what happens. I still think his peeing is behavioural, marking his territory and triggered by the strange cat & dog scents, but maybe going back to the old litter might help. Worth a try, as he was doing pretty well for a while. Hope it works.