My battery had also become swollen and the top right of the screen was lifting. Used the iFixit battery replacement kit and the anti-clamp device opener. For the battery removal, I used the isopropyl alcohol, but I also used the included suction cup as a stand and had the heated iOpener on the back of the phone. I think this helped loosen the battery as well.

This guide and tools made this job really easy and not frustrating at all. Screen was undamaged and worked perfectly after the battery was replaced (I did check it before it was all screwed down/resealed).

Thanks for the great guide and kit!