Back about 30 years ago I tried conibear boxes for cats and had nothing but refusals. They became illegal with all conibears in WA 25 years ago. I started trapping in OR and gave conibears a second try because I wanted a dog proof set for cats. Sounds kind of counterintuitive, I know, but I set them in trees about 5 feet off the ground with a very small run pole. They worked great but not with a box. I had a way of setting them up against the tree with the bait right against the back side of the trigger.
The trouble with boxes is the cat has to commit to sticking it's head into the box. A lot of cats won't do that. I think you could get the same effect as my set by making a very short box so that there was no space between the bait and the trap and there was minimal box in front of the trap. Basically, you are trying to make the cat grab for the bait without having to stick its head into something.
I nailed the bait to the tree and rested the springs on limbs, so the trigger was right up against the bait. The springs of the trap were wired tight to those limbs so that when sprung the trap jumped out towards the cat. I think you could do the same with a box. I do not like the idea of setting on the ground, however. Just asking to catch a dog. My run poles were angled so that the trap was at head height where the cat reached it. I'm not trapping OR now, but I believe the set would be illegal there now and probably most States. It did really work good though and never had any problems with dogs getting in it.