A float tube will separate the barrel from the front hand guard contact.

Any hand guard system that is still using a front end clip to the barrel, and you will need to sand bag the forearm up as close to the upper receiver to minimize how much you are flexing the barrel, and even disturbing the barrel harmonics.



Barrel harmonics,
As the bullet is being driving down the barrel, the barrel is going to move in a oblong path circle, and the bullet is going to exit the muzzle somewhere in the path of the oblong circle.   When you are tailoring loads, you are trying to get the bullet to exit the muzzle in one of the end points of the oblong circle constantly, which is when the muzzle is at it stillest.  When the bullet is exiting during the longer oblong path of end point to end point travel instead, you get a bigger spread.

As for in your case of free hand or benched up with a bipod on the end of the hand guard instead,  This is the same as bedding in a barrel to the end of the stock  (used something in rifle that have very thing barrels),  Here you are trying to minimize the barrel from moving so much in the lower oblong of the barrel/ muzzle harmonics movement, and then come up with a load that will exit the muzzle on the lower stationary moment.

So free hand with your forearm, the barrel/muzzle is free to move in it oblong circle.  
On the bipod, then the lower oblong path is semi prevented instead, and the barrel will group differently.

Thicker barrel will help slightly, but without a float tube to allow the barrel to float,  differences in the input to a barrel at the front guard clip to change the harmonics of the barrel (yes, even a bull barrel), will end up with the barrel shooting to a different POI.