Seeing a few thing on the groups that has me concerned, being the muzzle harmonics are not holding the same for all the groups.
On the bottle left group, barrel harmonics of the muzzle is 2-8 for the oblong muzzle path, while this does not hold for all the other groups instead.
That right hear tells me that the Barrel that should be free floating, is seeing some other influence on it to change the harmonic through the different groups
So by the numbers,
Pull barrel, give it a good cleaning with chamber and bore brush to knock off what you can from the leade and crown burs, then get the bore dry. On the barrel extension ramps, give the once over if they need to be polished or not to remove any end of ramp burs on the inside of the barrel extension. Also do a quick check on back end lip of the chamber to make sure that surface has a slight bevel, and not a sharp once that will be scrapping the brass on loading.
On the brake since it can effect harmonics, really need to shoot a few groups with out the brake to begin with, then you can stick is back on to see if it causing problem afterwards. Again, the weight of the brake on the end of the barrel will change the harmonics of the barrel to start with, and then some brakes are really bad about effecting the travel of the bullet through them as well.
On barrel install, moly grease on the threads of both barrel nut and upper receiver socket and on the inside surface that the barrel nut where it will be making contact to the front of barrel extension ring surface, then install the barrel nut to plus 40ft lbs. Hence 35 as your start point, do not exceed 80ft lbs to get the top barrel nut channel dead center with the upper receiver channel so the gas tube is not binding.
On the gas tube and gas block, do the index thing to get the block passage to index with the barrel gas port, but only lightly snug up the allen bolts. Now pull the bolt off the carrier, and with carrier with key, dry fit them into the upper receiver to make sure that the end of the gas tube is indexed correctly with the carrier key, and the gas tube is free floating through the center of the barrel nut and upper receiver channels. If the gas tube needs to be tweaked to index it correctly, then bend in over the center of the barrel only. Hence do not rotate the block on the barrel to try to solve the gas tube not indexed, since this will mis-index the block to barrel gas port.
Now with gas tube tweaked correctly, pull the block bolts one at a time, use 272 loctite, and lock the down.
Now back to the barrel and with this being a button rifle produced production barrel, it going to take about 20o rounds before the barrel stress relieves and the rifling uniforms from live fire. If chrome lined barrel, don't worry about rifling uniformity, since that going to take over 1K or rounds since the bore surface is much harder, but should still only take about 200 rounds before the barrel stress relieves isntead.
On the mag catch, be sure that the threaded end of it is flush with the face of the mag release button, and once you do have a mag loaded, rasp the back of the mag off your hand to pack all the rounds in the mag to the rear. The rifle recoils will keep the rounds to rear of the mag as your shooting, but we want to make they all start at the back of the mag to begin with.
Now the pro/con, and we drill it in everyone head to keep the action lubed with CLP to combat the fouling that the rifle will build up (to keep the rig running), but for shooting groups, it's counter productive. Hence any CLP in the bore will take about 14 shots to shoot it out, and with CLP in the action, it going to get transferred to the bore. So any lube in the bore, will change the exit point that the bullet is leaving the barrel in it oblong movement.
As for the scope and mount, should not be a problem so long as you torque the mount bolts correctly with the surfaces dry (maybe a touch of rosin to make sure that the scope is not going to move in the rings under recoil) and as for before you clamp the levers on the mount, make sure that you have pushed the mount all the way forward on the rail in the U channel to clamp the mount tight against the back of the U channels of the scope rail so the mount is not moving the rail from recoil.
So at this point, without the brake installed on the barrel, go shoot groups, and pay attention not to just group size, but the Oblong patch of the group on target instead. Hence on this rifle, we can see that the barrel harmonics of the barrel oblong whip is 1 to 7 in it movement, and is the oblong muzzle whip of the muzzle change, then something has changed of the barrel tension/mount to the upper to cause shift in harmonics instead.
Simply put, the muzzle is going to move in a oblong circle path as the bullet is moving down the bore (counter rotation of the rifle twist) and to get the rifle to shot it's tightest, we need all the bullets to be exiting the muzzle at one of the end of whip points (crest and trough), where the muzzle is stillest in it movement.
And the muzzle movement is not a circle, but an oblong path isntead. Also to point out, most the time the path will not be up and down for it end points, but off that axis instead. Hence in your bottom group and in your top right groups end points of 2-8 o'clock and should not be changing, no matter that ammo is put down the barrel.
As for production barrels, again will take some live fire for the button rifled barrel to stress relieve/ rifling to unify, but should not be seeing a shift in end points of the muzzle harmonics. From that point, then just a matter of how tight the rig will shot with the ammo is being feed, and the reason that we reload to find the barrel nodes of where it will shot it tightest with the ideal hand loads.