I plan to put plastic around to keep dust contained.
Bought a couple dremel attachments this morning, 1" dia thin saw blade to cut drywall into sections (drywall saw is slow & messy) and will use vacuum hose as I go along, & wire brush attachment to maybe get out plaster from screw heads (don't know if it will be effective though), but I think I'll end up pulling sections over the screw heads like you suggest. Not looking forward to mouse droppings raining down on me.
I hope the new suspended ceiling will help keep down the mouse population should they decide to move back in. When I moved into this 200 yr old house about 6 years ago, there was a suspended ceiling in this room which I replaced with drywall. Now I know why it was there!
My two cats are worthless. Don't want to put D-Con around or they might find a dead mouse and eat it. The spring loaded regular traps work somewhat. Along with the dremel stuff, I splurged on one of those electronic mouse catchers - $24 at sears. That should be fun.