Another data point: to be safe, I used the iOpener according to instructions (30s, ~900W microwave, the iOpener just started to expand a bit) and added some isopropyl alcohol. The battery came out without too much effort in a few minutes. No reheating needed, used the spudger from the kit.
The pre-exiting adhesive seemed good enough still, so I didn’t bother removing and re-applying.
Twisting sideways didn’t do it for me, but sliding along the edge did. However, at first I didn’t realize that the pick was between the motherboard and midframe, rather than between midframe and back cover like it was supposed to. This led to breaking off a spring-loaded connector on the motherboard, connecting to an antenna (I guess) in the back cover. So far I haven’t noticed any reception issues, but I can’t say for sure.
In essence: be careful to get the pick towards the back cover, and not “straight in” under the midframe.