OP, does your rifle fit you properly?????
One thing I've noticed about new rifles lately is that they all have 13.5-14 inch stock lengths.
If you are shorter in stature or have shorter arms, that rifle won't fit you properly and felt recoil will be greater. Especially off a shooting bench. Your body is anchored in a chair while shooting off a bench. Only your shoulder is taking up the recoil.
You don't mention what cartridge your rifle is chambered for either.
T3 LIGHT. The name says it all. The less a rifle weighs, the more felt recoil on the shooters body will be noticed.
One thing though you will never feel or even hear the shot you take at a deer.
As for the bbl on the T3. They aren't any lighter than any standard rifle.
IMHO, muzzle brakes can cause a lot of extra issues you really don't need. First, increased noise levels, second, increased length. Third but not least, you can buy a heavier rifle, chambered in a cartridge you can handle for about the same amount it costs to mount a good brake. Not all of them work well, except in the minds of their makers.
The difference in felt recoil between the 30-06, 308Win, 270Win etc, is negligible, given that pressures and bullet weights are similar.
If your rifle is sighted in, you need practice and more practice OFF the bench. Bench shooting is fine but it lies to you, every time. You need to learn how to shoot well OFF HAND, from a kneeling position, from a prone position and a few other even more awkward positions.
In my old age, I have relented my capabilities to using a walking stick/monopod for off hand positions. I use a rest of some sort for every shot over 100 meters.
A really good, cheap target, is a package of circular pages, about 17 cm in diameter. That is the kill zone on game from deer to moose. Old aluminum foil pie plates work very well to. Set these targets out at different ranges, remember how your cross hairs in the scope look on target at those ranges. That is a very good way to measure ranges out to 300 meters as well. Some people get very good at this.
By the way, I absolutely hate shooting off the bench. I only do it when sighting in a rifle. Then, unless something seems awry, it's all done to imitate field conditions, where it really counts.