The bad news was that the adhesive strip ripped on the logic-board side. The good news is that recovery was not as difficult as I thought. By using a hair dryer, and some very patient wedging with a credit card, I was able to separate the battery from the adhesive, and then remove it. Some simple cleanup with tweezers got the adhesive sticking to the case. Just make sure you get it right on the edge side, or this technique will be a lot harder to pull off.
I also skipped all of the screen-removal steps and had nary a problem. Just rubber band the screen around whatever it is propped against and I believe you'll be fine.