How can I keep my shoes safe while resting my feet on a multi-pitch?
It's simple: Don't take your shoes off.
If your feet hurt so much that you can't wear your shoes at the belay, you are either working a very, very difficult line, or you've made the mistake of wearing way too aggressive boots. Most multi-pitch lines are not overhanging and can be negotiated with simple flat-lasted shoes.
That said, if you do need to take your shoes off, you might consider buying HangDogs from http://outercoreclimbing.com/.
Alternatively, simply loosen your laces and tie the ends tight around your ankle (a square knot works well) before removing your shoe.