If you haven’t shot much centrefire before, a .308 does take some getting used to.
Add the fact that you have a known very light rifle, and it’s no surprise you’re finding it uncomfortable. I struggled with .308 when I started with it, and that was with a substantially heavier gun than the T3.
The very best solution is practice and improving your technique. Technological solutions often ultimately cause more problems than they solve.
Start with simple things: shoot off a front and rear bag, rather than a bipod. Don’t use the sniper cross arm hold - grip the fore stock with your left hand (as if you were shooting unsupported). Make sure your body is lined up properly. Make sure you have a good cheek weld and your not having to raise your head off the stock to get a clear sight picture. Make sure the butt is tight against the fleshy part of your shoulder, not your collar bone. Get someone to watch you shoot and see what you’re doing.
I am a self confessed recoil wimp, but I can now shoot an unmoderated .308 perfectly happily.