Some thoughts
Get the basics right, like the mentioned firm grip on forend and pressing the gun back into your shoulder, firing each shot off with as identical hold and grip as you can.
A suppressor / brake may or may not help the gun shoot more accurately, but it will change your point of impact. It all comes down to trying it out on the range. A break or suppressor helps more by softening recoil and thus reducing shooter flinch I suspect - so a pleasant gun ends up being a more "accurate" gun. Which is why .22LR is a great practice round.
The reduction in muzzle climb is not that helpful, at least for accuracy, as the main part of the muzzle climb that a suppressor / brake reduces is the climb that occurs AFTER the bullet has exited and the fast gases rocket out. Any added weight to the end of the barrel will of course reduce climb from any source.
Your big scope put on a higher mount along with a cheek riser pad may put the barrel more in line with your shoulder and so reduce climb... and maybe remind you of an AR you may once have owned.
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