Ideally, I'd like to be able to get all notifications on the watch and only on the watch whether the phone is on or not, except when I'm not wearing the watch. Then then can go to the phone. I only take off the watch at night when I'm sleeping, so normally the second part isn't an issue, except I prefer to be able to receive phone calls at night in case there is an emergency or for when I'm on call for work.
Yes that is exactly what I would love as well. My exact situation too.