Never considered fishing line, that's an excellent idea. Thanks everyone.
I want to rig a bit of a handle on my woodstove so that I can hang it, move it more effectively once finished cooking to start cooling it off, and to maneuver it on its side, as the circular frame is also useful as an enclosed grill over an open fire for larger items like casserole dishes and fish.
My stove is a home-made IKEA one, so it has tons of holes punched in it already for the line. I'll post some pics once I get it set up.