Oy...sounds like quite a sticky mess of a situation! If I were in your shoes, I'd be calling a professional exterminator. Explain that you have live rodents you want to KEEP alive, so gassing the house is not an option. Not only should a pro have other (more effecient than one trap at a time) solutions for getting rid of the mice, they should be able to help you find the source of the infestation and close it up.