You could try tearing the upper apart. Squaring the receiver face with a lapping tool, the barrel would have a true face to mate to. Then clean the outside of the barrel extension. Clean inside the upper receiver. Grab a caliper, and measure the inside dimension of the upper receiver. Then measure the outside of the barrel extension. Subtract the 2 dimensions, if the difference is less than .0025 inches or less. You are good to go just loctite it in or rocksett the extension into the upper whatever you decide. However if the difference is greater than .0025. Take the difference and subtract .002 inches to compensate for the clearance needed for barrel extension into upper. Then divide your answer by 2. Whatever number you come up with is your required shim thickness. Then make a trip to the local industrial supply house and get a roll of stainless steel shim stock in the correct thickness you need. Cut a strip to wrap around your barrel extension, clearing the feed ramps. Make sure the seam to the shim is horizontal to the barrel indexing pin. Get the seam as small as possible. Put a piece of tape or something to hold it together to get it started into the upper. You could use heat to make it easier hair dryer, heat gun whatever. And fit the barrel extension in. Torque barrel nut to spec.
