I had no idea this was a thing with rodents. Just curious if they had a room instead of a cage, could they be litter trained? You mentioned they would pee in them but what about poop in them?
We took care of a couple of classroom rats over the summer once and I really enjoyed them. But we had an extra room that we weren't using at the time and let the kids let them out of their cage fairly often. They weren't in any way litter trained so that was a big lesson for them.