Any chance the piggy cat is bigger than the small cat? We've had members do either collars with chip code that operate cat flaps, or just a feeding space/box of some kind with a door that only the skinny cat cat fit through. I wouldn't lock at cat in the bathroom all day, just for the time for her to get an extra meal. I was lucky at one point that the allergy kitty could jump up higher than the fatty. So I fed her on the counter.
If you are looking at novel proteins to feed for allergies, both duck and lamb are high calories, than something like rabbit, kangaroo, venison. Chicken thighs are higher fat than chicken breast if she can eat chicken and you are making your own. I didn't spent time on allergy tests either, just tried one protein at a while until I figured out which she could/could not eat.