I used a hot-water bottle to keep the iPhone warm while prying patiently, though the moving surface added to the challenge.
Before that, I put the iPhone - screen facing down - to warm on the coffee cup heater (45°C) of an espresso coffee machine. Half an hour seemed more than enough.
A hot-water bottle filled with water at 60°C would do the job I think.
Later repeated the same heating before removing the adhesive strips under the battery (allowed me to extract each strip successfully, rolling it on the body of the spudger).
And also before putting the new display assembly adhesive under heavy book weight.
For this finishing step I tried iFixit’s Adhesive Cleanup Kit. The first pad of the kit, the Adhesive Tape Remover Pad, is soaked with a slippery solution that did an incredible job of cleaning residuals of glue and dirt. May I have to redo this repair, I would put less effort at the previous steps, relying on this pad instead, hopefully saving a lot of time.
This slippery solution doesn’t seem to evaporate. Obviously it needed to be cleaned if the new adhesive was intended to stick. That’s the role of the second pad, saturated with 70% IPA. Caution with the fluff that detaches from this pad, however.
Instead of peeling off the backing progressively, I found it safer to cut the bottom part of it with scissors, so that about 1 cm height of adhesive was exposed. This way, the sheet laid FLAT over the iPhone frame and could be centered accurately. Once precisely centered, I held the sheet in place with one hand, and with the other hand took the spudger and pressed down the bottom part of the sheet, to actually stick the adhesive to the frame. Then peeled off the rest of the backing as the pictures show.