Honestly, I have only shot it prone on the AR, so nothing really to speak of. It does noticeably reduce the recoil impulse on the 7RM, so I would guess the dust kicked would be significant compared against standard muzzle blast.
I have a SiCo Harvester 30 that I switch between my 7RM, 7mm-08 and my AR coyote rifle. I just switch the threaded insert from 5/8x24 to 1/2x28. It's a direct thread. Paid about $800 including the stamp a few years ago, not sure of the current price. It is attached to the 7mm/08 in my profile pic.
Not a .308, but for my 7mm-08, I load 160 gr. Sierra Gamekings over 10 gr. of Trail Boss and get @ 1050 fps out of a 22 inch barrel of my TC Venture compact. Very quiet with my Silencerco Harvester 30.