Wow - That was a bit more intense than I expected, but successful. My only recommendations are:
1) Use a clean and organized workspace with plenty of time, don’t rush.
2) Take your time separating, identifying, and organizing the tools and parts you remove.
3) Be precise with your tweezers and go SLOW when removing the adhesive. When your pulling the adhesive strips with your fingers, go very slow, then a bit slower than that. It will prevent a major headache if the strip rips.
Pulling straight down towards the bottom of the phone at a small angle worked well for me. I highly recommend taking your time to prevent breakage. I think I spent over 8 minutes on each strip just slowly stretching it out so it would not break. Just keep it straight and dont twist. I was able to remove both strips intact and thus did not need to pry the battery. Because I was able to do this method, I left the screen attached and saved a few steps (I was not trying to save time, just did not want to create additional problems by removing and reconnecting various ribbons). I think slow and steady will be your best friend. I did not heat up the adhesive or case.
I skipped this step and just affixed the screen to the Iphone box with a rubber band during replacement. I decided to take this risk to prevent some of the other issues that have been discussed when removing the screen. I understand it is risky because if you slip or need to use any significant force to remove the battery, disaster awaits. On my repair, it worked out fine and I ensured that I took my time and kept the bottom of the phone held to the worksurface.