It seemed to shoot okay before but i never did a proper test. Then I mounted a new scope and got a 3 inch group at 100 yesterday from a bench rest when I zeroed. Been fiddling with it since.
I've been shooting really lightweight bolt rifles for a long time and these are almost half the weight of those bolt rifles, so probably benefit from the same techniques and then some for the really lightweight UL-ULs.
A few things to check off trying:
Make sure your rest is soft enough to dampen any potential to bounce. I put a folded towel on mine for the handguard to rest upon.
A rifle half the weight of another will move twice as much as the bullet moves down the barrel, all else being equal. No way around that.
Use your body to add weight to the rifle. For best shooting, I lean weight-forward into the rifle butt to help minimize any rearward motion of the rifle before the bullet leaves the barrel.
To "add more weight", try holding the handguard while leaning in to the rifle butt to gently lock the rifle in between your shoulder and hand.
Hold the grip very loosely, or move your thumb over with your other fingers. Too firm a grip can add torque to the rifle while firing.
All this is easy to do in the field as well. If shooting off a pack, they're usually pretty soft, and a hand under the handguard dampens bounce. A light grip on the handguard allows leaning in, weight forward.
Lots of dry firing using these techniques is helpful, I think.
Heavy rifles largely take care of themselves compared to these rifles...obviously why benchrest rifles are so heavy.
Last point I guess: It doesn't sound like you've actually confirmed that your barrel shoots either of your loads well. That would be a good place to start while you're working on other stuff. I know my Shaw has been pretty picky.