RE: uneven elevator
Totally flat won't help. You'll need to bend it in the opposite direction and THEN apply the heat.
As you bend it, the covering will wrinkle. Just heat until the covering smooths out again. You'll need a heat gun for this - a Hair Dryer won't work.
PS, aviod getting heat near the edges of the covering. The edges can pull loose. If you must get close to them, lay a wet cloth on the seam to protect it from the heat