1.) In the Activity app on your iPhone, do you see Stand time reported as 0?
Yes
2.) When starting a no goal Walking workout on your Apple Watch, do the timers auto pause even if you're moving?
Yes
3.) Do you sense that notifications come in unreliably?
Yes
4.) Does the Wrist Detection problem persist even when you ask a friend or family to wear your Apple Watch?
Yes
.... turning off Wrist Detection has solved points 2 and 3 for the moment, but obviously it's not an acceptable long-term solution.
I have talked again with Apple Support and they got me to send them some Watch logs after I made the exercise pause happen and then synced with iTunes.
So hopefully we are working towards some identification of the problem and an ultimate solution.