Those are not exactly easy to achieve goals.
There's rather a large difference between a rifle that put 5 into 3" at 500 yards once or twice in a range session, and one that does it every time, and with a consistent cold bore shot.
A good part of that consistency stems from how the rifle fits you, and your comfort behind it.
You'll never know what you're missing until you try it.
But I digress, you can lead a horse to water...
And in regards to the tac 21, every smith I know will not accuracy test a rifle in one. They'll use a different chassis, or stipulate a full glue in before testing.
It's not rocket science, the scope isn't attached to the action. The action is attached to the scope through the chassis via the action screws in essence.
The action certainly shifts in the chassis to an extent, the recoil lug wouldn't work properly otherwise.