IMHO after lots of years and effort dealing with a SHOTGUN flinch there is nothing more likely to worsen the flinch that not knowing if the gun is going to fire or not.
If tried, please let us know how it works out.
And after Dan Lammers tuned the locks on my Smith, trying to use a creepy, heavy, rough trigger is absolutely hopeless.
Drew, with the technique I used, it's all about conditioning and concentration which eliminates apprehension. We've all seen a skeet shooter just about topple over after a ftf after bracing for the shot. I started with .22LR and once no flinch there, went to the bigger calibers. It takes time and repetition. With shotguns, I'd start out with .410. Gil
