I've never worked cherry but have heard it is not very strong under compression.
To answer your other question - the sign of a belly being overpowered - if you look closely at the belly, you will see chrysals, which are just small cracks that indicate the wood cells on the belly have been crushed and damaged. By the time you see this, the damage is already done, and you will likely have a bunch of set that goes along with it.
Like I said, I've never worked with cherry, but trapping the back may be a way around this. You will want to tiller slowly, and might want to try the "no set tillering technique" if you are concerned about damaging the belly. There are threads about this technique on the forum.