Sounds like you have a real problem there. It's amazing what these little critters will do. Hopefully you will hit on a set-up that works.
I have problems with mice almost all the time, except during the summer. With an old house (as you must know) they find ways in everywhere. I have to set traps for the fall in the cellar and attic soon, any mice in the living areas are toast, one of the benefit of having cats. One of our cats will not only catch the mouse and kill it, she eats it as well, kind of gross when she crunches on the skull and we find a little gut pile.
This summer the other cat kept staring at the Harman, turns out there was a bat in the firebox, must have found a way around the chimney cap.
Good luck with your efforts,