After a week of this nonsense, it occurred to me that maybe I could start over with a physical SIM card. I chatted with frontline support again, and he said he was positive that would work. (So why didn't anyone suggest that?!) I couldn't use the old card, because it was clearly beyond their capabilities to reactivate a perfectly good SIM card, but I was able to buy a new one at Best Buy and complete the process in about five minutes.
I would have swapped the card in the first place and been blissfully ignorant of the eSIM fiasco, but I somehow had it in my head that the iPhone used a smaller card than the five-year old phone it was replacing. It may not be eSIM's fault, per se, but if the design is dependent on carrier competence, it's fatally flawed, as far as I'm concerned.