@Dave - So it turns out that not only did the rep add a number with my AWS3 IMEI and EID to our account, but instead of "parking" it SHE ACTIVATED it manually, but I didn't know that during all the times I've tried to set up cellular today!
I just told her the Apple Watch app needs to activate it, and the line with my EID and IMEI was only supposed to be parked. Right?
The Apple Watch app on the iPhone was still failing to set up cellular, and the last time she'd had me try skipping cellular, to set up later on the phone, and we let the watch finish syncing everything else. Then we tried to set up cellular with the Apple watch when it finished setting up everything else - but when it failed to activate again she said, "that's not possible because I activated the watch."
She is going to see if we need to wipe the Apple watch completely in case the eSIM was activated or filled in with something, or whether she just needs to delete the active device's EID and IMEI and do it again but only park it. Then I can try again.
On my account the "view profile > account users" screen showed 12 users, including the new AW phone number, and device management page showed just the 7 iPhones and 4 iPads, but not the AW. So, I await her return call.
EDIT - (*^^%#)(&!!!!!
They asked me to reset the AW3 and start over, AND I RESET MY S2 AW BY ACCIDENT! - NOW I HAVE TO RESYNC MY PERFECTLY WORKING S2 WATCH AGAIN TOO!!! ARGH!!!!!