Ok the hot washcloth (actually dish towel) plus sliding a credit card under the battery worked. Old battery is out. Now to attempt getting the new one in. The old adhesive strips were really stuck down pretty good and I think there was no way to pull them out with the recommended method, or to get enough alcohol under the battery to dissolve the adhesive. Heating is the only workable method and maybe some kind of thin metal shim tool would be helpful in cases where a credit card is too thick.

Both of my strips broke, isopropyl alcohol didn't help. I got dental floss under one corner and loosened a few mm after which progress stopped, i.e. it got stuck hard enough to break the dental floss. I don't have any monofilament. I will try heating the back of the phone, using a washcloth soaked in hot water and sealed in a ziploc bag as a heating pad.

Both of my strips snapped. I put in 91% isopropyl alcohol and waited a while and it doesn't seem to have helped. I may be able to find a hair dryer here but it sounds unlikely to be hot enough. I have a proper heat pencil which is the right thing to use for this, but it is not here, and I can't easily retrieve it in reasonable time to return the phone to the owner. I will try the dental floss method.

Oh what a pain in the neck this was. The suction cup is a hit or miss thing. But if you press down on it all over (center, edges, and the in between part) then it will stick reasonably firmly about 1 try out of every 5. When I did that, on the "good" tries, I was able to get the screen to move a tiny bit, not enough to put in the spudger. There was enough space for a utility knife blade to stick in, though it was a 2 person, 3 handed operation. I pulled the screen up (a fraction of a millimeter) and got another person to slip the knife into the crack while I was pulling. Then I was able to use the knife to get 1 corner of the screen opened enough to use the spudger the rest of the way. @flannelist gave very helpful encouragement in the Q&A forum. Anyway I still have the rest of the steps to go, so let's hope they are easier.