I managed to remove the rear cover without a heat gun. I used the ifixit opening tool, and got it in between the outer metal frame and the glass cover, and slid it around the phone. With light pressure it was easy to lift the glass cover slightly without damaging it. I then used the flat end of the spudger to pry the cover from the adhesive on the battery. Replaced the camera as shown, and just stuck the rear cover back on as the adhesive was still intact. Although I will probably replace the rear cover adhesive just to be safe and preserve the waterproof features.
I also had a white screen, followed the guide step by step, made the repair easy. I do agre with one of the other comments, a 000 phillips screwdriver worked way way better than the 00.