I have an older P07 so I can't speak about the new ones and their back straps.
Let me tell you about my M&Ps and their back straps so you can check your "reaction" and see if it makes a difference for you.
When I got my M&P, I tried the different back straps and the largest one felt the best. When I got my second M&P I put the largest back strap on it, too. At the range, they felt just fine and I didn't notice anything amiss. However, while dry firing, I noticed a problem.
If I was looking directly at the target in front of me when I brought the gun up the sights aligned perfect, just like they should. If the target was off to the left, right, high or low, when I brought the gun up, the sights would be "off" and I'd have to make a secondary adjustment after the gun was up. I've never had this issue with the 1911's. When the gun was up, the sights were aligned and on target.
I went back to the house, got the other sized back straps and took them out to the edge of the woods behind my house. I put the medium sized one on and the sights were closer, but not on the target when the gun got there. I put the small back strap on and the problem was fixed. When the gun came up, the sights were aligned with the target.
It may not be an issue for you, some folks said I just needed to practice more and the problem would go away. However, I have more than one brand of gun and I wanted to make sure the M&P and the 1911 worked the same for me. Try yours with the different sized back straps and see if one works better than the others vs. feels better than the others.