Sometimes crafty supplies come in handy for other household uses.
Alas for my new shoes - unpleasant sticker residue under my heel, and then the insole came away. Luckily I had Best Cleaner Ever - I sprayed two spritzes to quickly dissolve the glue, and wiped with a paper towel.
Best Glue Ever re-attached the soft foam insole. Harsher glues might have dissolved it. Plus I didn't want to end up with the feeling of bumps under my heel. I simply put a line of tiny spots on the bottom, and allowed it to dry for about a minute (I'm not very patient, so it's good that it dries fast). Then I pressed the insole back in place. Now my new shoes really do feel like new.