All the mesquite I have turned came from the area around San Antonio and it is one of the most stable woods I have ever turned. It normally doesn't move much after turning even when turned green. That is a nice bowl by the way and I can see why you are well pleased with it.
Don't give up on turning in the expansion mode. It can work well. Maybe turn your first bowl a 2nd time and apply finish and see how much it moves.