Don't know about ratproofing papier mache, but an easy and  humane way to catch rats and mice is to get a large plastic/glass jug/jar, put some food at the bottom, and then prop it up at an angle (I'd put some heavy objects around it so it doesn't roll away either)--the rodents can get in, but because of the smooth sides, they can't get out again.  Then, all you have to do in the morning is take your catches and release them outside somewhere (preferably a good distance from the building so they can't find their way back in again).

Or you could get some cats . . .

+1 on the use of a non-organic adhesive.

Use either methyl cellulose wallpaper adhesive (made from processed wood), or regular white craft glue (PVA, polyvinyl acetate) diluted with water.

Varnish or polyurethane as a sealer should help, too, but not over a food-type adhesive.

Sue