I feel like, a lot of the time w/cats (at least when I've lived w/them) it's like that old principle: GIGO, garbage in, garbage out, so... at least in theory better food for the cat means less gross, ahem, output. In case that might in theory make litterboxes less gross (it kind of did for my ex, who said that when he'd housesat for ppl w/cats b/f he'd been too grossed out to deal w/the litterbox previously).

Good luck finding a new place!! That really sucks to have to move when you knew you wanted to stay. :(