We have been camping at Willow Springs in March and was able to find a spot that was comfortably away from others. Its a pretty large area. Some spots are more easily accessible than others and those obviously get taken the quickest. If you're not afraid of pulling your RV down some bumpier roads you can find some great spots that our less crowded.
Willow Springs is busy quite often as it's easily accessible and there are mountain bike trails at the end so quite a bit of traffic. The nice thing is it's a nice road to go up and down. You might get lucky the earlier in March you go. By April I would consider it pretty busy for sure.
Have not been to Moab in March so I wouldn’t know we were there in the fall and it was packed. If it can be arranged try to get there Monday or Tuesday to find a good spot, closer to the road better the cell service.