Have you considered "crate training" the cats? When my male (not neutered) cat brought in a near death kitten last April/May, we put him in the biggest dog crate we own, with some towels, a litter box, food & water in dishes and a blanket on top, and kept him in there for 2 months under the kitchen table. (It's one of those tall tables, with three tall chairs, against the wall. He got better in a few days, and didn't mind his safe space. DD's took him to their new house, and he will be 1yo next month. He had no trouble traveling in the cat crate and has perfect litter habits.
I also shut my cats in the basement when a repairman is here, and I even put my male cat in the pantry in the basement when I have my Salsa Party. He doesn't do well with strangers, and I find him two days later, used litter box, sitting on the cat mat where I left him.
They CAN be trained. You gotta get past the silly cat people who think it is charming that their cat misbehaves. I love my cats, but I don't like a disobedient one.