I know the standard sporter barrels have an insufficient diameter to thread 5/8-24, and it may be cutting it close to get a shoulder that a 1/2-28 brake could be tightened against. Clamp-on brakes are available for sporter barrels from a few manufacturers like Kahntrol. They're pretty well regarded though I've never used one. Another option would be to swap the barrel for one with a threaded muzzle, whether it's a flared barrel like that on the Axis SR or a heavier contour. A heavier barrel would necessitate a stock change though.
Axises are very lightweight guns, so a part of the problem could be that there isn't enough mass to hold the gun relatively still during recoil. There are a number of threads on increasing the weight by filling voids in the plastic stock with epoxy or Rockite. A heavier stock could also be available from a few aftermarket manufacturers as well.
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