I would guess that the difference in grip shape between the glock and m&p, is causing you to grip them differently. Sounds like you're not getting as much contact with your support hand on the m&p, hence the to the left recoil. You could probably train out of that.
On the g34, I really like mine. Very controllable rapid fire and follow up shots. The barrel length itself will give you slightly higher velocity, but more importantly with a longer barrel comes a longer sight radius. I have limited experience with other glocks, but in comparison to a 17, I would give the 34 an edge.
My question is, why not use the g19 if you shoot it well?