This is _so much worse_ than I had imagined. I'm really glad I decided to do a little digging around before trying more things. When just signing the second iPad up presented me with an error message, I was going to cancel the account on the first iPad and try again. However, the experience this guy had with turning off an account on one iPad and then starting up on the new one suggests that this is not a brilliant idea.
Worse, when this guy had ATT transfer the account from the old SIM card to the new one, ATT said that the old SIM card might not work any more and need to be replaced.
I have to wonder what the thinking is behind this. I'm not even a corporation. I'm more or less in the situation this guy was in, updating hardware, with the additional complication that the old hardware is not being retired, but instead repurposed to another person in my family. I might well want to use the cellular on both at the same time. Making me have a separate e-mail for each of them is _profoundly_ annoying.
I have a secondary e-mail account. I guess I hope ATT gets this figured out before the 3rd round of hardware comes out.