Doppler is the technology of the 1980s and before. Doppler is a pain because as you say, the water is either too rough or too smooth most of the time! And it usually doesn't like to be near a ship etc.
Modern aircraft with SAR modes don't use doppler (eg EC225) - instead its inertial with GPS (double GPS for redundancy). This makes the auto-hover rock steady and unaffected by sea state.
Radalt hold is generally fairly "soft" so it does not bounce up and down with the waves. EC have chosen to trigger "fly-up" mode when height is more than 30' below datum height, so if waves are greater than +-30' (ie 60') then it might have a problem, but that is a fairly wild sea. Bristow will be getting SAR EC225 into Norway in a few months, it will be interesting to see how well it works in reality.
HC