First, I used a wheat bag for my heat source to soften the adhesive (cloth bag filled with wheat grains, which you heat in a microwave, usually to apply to an arthritic joint for pain relief). Retains the heat for a good time and provides a base on which to work (a bit like using a hot water bottle, but without the water and a lot more stable !)
Second, my adhesive strips broke before I got anywhere close to the battery corner ! So I used dental floss. Starting at one corner of the battery, using a sawing motion to reach the other (nearest) corner, then came down the length of the battery. The floss broke about a dozen times, but after about 15-20 minutes it had cut the battery clean away from the adhesive.
In another guide there was a reference to the screen being pulled away from its frame? This was happening to me, so used very small amounts of superglue between screen and frome, applied using a cocktail stick. Left it for 24 hours. Worked fine.