I've never had this kind of problems before. I've recently played a lot with 3 fingers (right hand). When I play with 2 my arm rests on a body of bass but when I'm using 3 it's hard to play with arm in that position. Arm tends to go off body (to have a straight wrist) when I play with 3 but than I lost balance, bass starts moving around and I can't hold the bass with left hand because its focusing on fretting not on keeping balance(that has to be like that!)
What do you do? How do you balance a bass without putting right hand on body? Maybe a good fat leather strap will help?
Some basses have terrible balance, with the too much weight towards the neck, causing the neck to want to "dive" towards the floor.
If this is the case, there are two things you can do to correct it.
The first is adjust your strap. The higher the better (well, that was my experience). A better strap as you mentioned might also help.
The second is to move the strap button so that the bass is more balanced (requires drilling ... I wouldn't risk ruining my bass personally).
It might also help to push your arm against the top of the bass as you play, but I would hate to do that.
New problem 
