But how would you amusingly freak out cats if the vacuums were silent?
I wouldn't do that. I love my cats.
You could have all the EMHs wait near the litter box, and when the cat goes in, turn their sound on again.
Nope. The EMHs can damn well clean the litter box and take out the garbage (would have to put some kind of restriction on the distance they could go with their mobile emitters so they don't escape, of course).