I'd say Charlie is onto something.
1) I learned from a bowyer/tuning source that if a bow is cut to center or beyond, as he put it, it will "require a stiffer shaft to tune, but those arrows, coming off a finger released string, aren't sure which way to paradox, shot-to-shot," so shimming out the side plate a bit helps improve flight & tuning.
2) If you're on the edge of weak, shimming out the sideplate will make the arrow 'act' stiffer and may improve your flight considerably with negligible impact on where you're hitting!
Otherwise, you're going to need to have that "excellent" form, release and follow-thru EVERY shot or as you said, that 3rd/4th one will show you're not in the middle of the bell curve of proper tune!
Under field conditions, that "perfect form" seldom happens and wounding can result!
3) shot to shot inconsistencies are best fixed "shooting the bale" at 5 yrds or less, over and over, focusing only on your form throughout the shot. I personally find it boring as sin, but, it sure seems to get me in the "groove" better, faster.
300-400 shots! Wow! I wouldn't be able to move for a week!
If you want to "experiment" with side plate shimming, just get some plastic electrician tape and build up layers with a small piece of cereal box cardboard under it and a few layers of tape build up quickly. 1/16" can make a big difference... and when you're done, it peels right off. No harm, no foul. Measure the thickness if it helps and then peel your sideplate up and put a bit of toothpick, or other shimming material that thickness under the sideplate, glue it back and walla, you're done!