I'm not taking it as rude, no worries their.
Most of my rifles 30cal and down have a suppressor on them or I have the ability to move one to another. All of the suppressor that I currently own (in my possession, still have some at dealer). All have more push than a rifle with a brake. Nothing crazy, when you are looking for impacts at 300-400 yards shooting bullets at 3k+ fps. I can see the difference, this is a match setting, don't want to set the wrong stage. Now with that said, a suppressor is less recoil than a bear muzzle.
I'm not one 100% certain of the can that was used on the 338LM. It basically happened to me 3 X. 2 of the 3 were with the same rig, it was a Barratt Mrad. The other was a custom builder that I don't remember. I told several of my shooting partners that were in the match with me to put on your glasses, before you shoot that rig. Several of them thanked me for the warning afterwards. To the best of my knowledge both of those cans were over 12" in length. That could have something to do with it. It could be that most of us were shooting 18-20# 6mm rifles with brakes on them that have very little recoil to deal with. Or a combination of all the above (everytime we shot it was prone).
TBAC is building a can with a brake on the end of it. This is for their 50cal line. I have seen one made in 30cal, I have an email into them to put me on the list when they come to market. It will be a few points higher than the plain can with the recoil impulse reduced significantly. I have an Area 419 Maverick in jail right now and will order the TBAC today if they were to say it was ready (I feel TBAC makes some of the best, Ray and Zack are also shooters).
Shooting from the sticks might not be as bad. Depending on who makes the can, will impact the performance of sound and recoil impulse. I'm a little basis, I shoot a lot of matches and I look for advantages. If I can watch my impacts up close, I can't make connections. So take my thoughts with a gain of salt. I'm very picky about some of these things for the reasons listed. I'm not a master at any of this, I do send a lot of rounds down range.
Before my Africa trip, the biggest rifle I owned was a 338LM. I have not had the opportunity to shoot a suppressed 375cal or up. So I am assuming what it would feel like based on my experience with everything I have shot at this point. Just want to make sure we are on the same page.