Both adhesive tabs broke for me. I ended up starting with the hairdryer then trying floss and then a plastic card which was too flimsy. In the end I used the plastic wedging tool to pry the battery up and hold it there. With the battery raised, on the side closest to the phone edge I was able to scrape the adhesive strip together enough with the tweezers and then my fingers to pull at it laterally stretching it so that it came away in one piece. The battery was slightly dented and bent, but not punctured at this point. The second strip near the logic board was much higher and necessitated bending the battery much more and just holding it there. I couldn't get the battery up enough for fear of a puncture so I just held it there as the adhesive slowly detached itself and in the end the battery just popped free. Not sure if the warming from the hair dryer made any difference.
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