I'd suggest a squeeze bag for the rear / back or stock. This way you can control the slightest movement needed to raise or lower the muzzle, w/out needing to stop. Remove yourself from the shooting position you're in, find another rear bag get back in to position, realign you sights, etc. I had this one suggested to me during a class, combined with a good bipod, really made a difference in my overall shooting. And yes, Semi autos are capable of sub-moa.
https://www.amazon.com/Crosstac-Tact...rifle+squeeze+