Ok, so I did it wrong, but it was fixable. Backed up old phone before unpairing, but since this was at the end of the day and I was hardly running laps, it wasn't a huge deal. What was a huge deal was that my health data disappeared (even though I did an encrypted back up on iTunes).
So, before I threw in the towel, I decided to back up the old phone again, this time to iCloud. I wiped the new phone and restored with the iCloud backup and my health data was back.
I only had one choice for Watch back up, so I used it. End result was that I lost about 100 calories from my move ring, which kept me from completing the ring by about 80 calories.
But, I had over an hour of exercise and 14 standing hours, so I wasn't harmed there.
But dang it. There goes my perfect month.
So, if I were doing it all over again, I'd do like stated above:
Unpair watch (after completing all rings)
Back up old phone to iCloud
Activate new phone and restore with iCloud back up
Pair watch to new phone (and you'll be asked to restore Watch first)