Going to put a sledge hammer to my M&P Shield

[Fastbolt]

I think "trigger over-travel" is creating your problem. This is the rearward movement of the trigger after the point of the release of the striker. It can hinder your follow thru to stay on target.

Probably your trigger pull is the same as my Shield, 7#. That much force is being applied by your finger against your hand holding the gun. When he trigger breaks, you're still applying that force against no resistance from the trigger, so your hand ends up jerking during the LONG over-travel. The problem comes from the fact that neither primer ignition nor bullet emergence from the muzzle are instantaneous after their initiating event. You end up jerking the gun off target due to over-travel unless you've specifically trained to overcome it, and that's not easy to do.

Just as a bit of trivia ...

Once, when I was attending some training put on by one of the gun companies, the students were told about an engineering project done by the particular gun company hosting the training. The purpose was to try and determine just what effect trigger over-travel actually had on a "shooter", versus what a "shooter" might "feel" it had on their practical accuracy.

We were told the engineers used high-speed imaging to capture the trigger stroke and the instant of ignition, and then how far the trigger was moved by the shooter before the bullet left the barrel.

The results of that test, using that make/model of that semiauto pistol, reportedly revealed that the bullets had left the barrel before the shooter could even finish pulling the trigger through the rest of its travel (or, through the "over-travel" part of the trigger pull). It was interesting.