Is your shroud "free floating", with no parts touching at the gas block? If so, it theoretically works by dampening barrel harmonics and perhaps by stiffening the barrel.
I've always wanted to do a "post tension" type of barrel shroud for the mini, like the Dan Wesson revolvers have. This would have the shroud actually bottomed firmly against an adapter that seated against the gas block. The muzzle is threaded, 1/2" Diam X 28 TPI for 3/4", for an AR-15 style muzzle brake . Then machine a tensioning tube to fit between the two ends. Basically, you stretch the barrel between two immoveable objects. Torque until groups shrink.
Anybody done anything like this?
Also interesting would be the AR-15 flashider with a lock ring alone. Just like the Browning BOSS, you could thread it in or out to tune. Unfortunately, this would probably not shrink groups with all loads, but you might be able to come up with a couple of loads that shot spectacular groups.
Or you could combine the two - start with the BOSS/flashider alone, then add sthe hroud as ambition dictated.