Your never going to get a panel cut perfectly straight unless you do it on a ban saw with a guide. The only way to cut your door reletively straight is by using some sort of guide to steady the blade if your using some sort of saw. Easiest way would be a plasma cutter, but who has one of these unless they are a metal worker.
You don't need to cut both panels on top of each other, sure it would probably work, but be a pain in the ars. Just cut out the rust and after you clean the edge and straighten it out with a file if need be. Then just place the peice of sheet metal you plan to cut the patch panel from on the outside of the hole and from the inside out use a rattle can of anything and spray the edge. The sheet metal will have the identicle shape of the hole needing to be patched. Just cut it out and weld it in.