Based upon the conversation and the photos, I think what you have is a "Muzzle Stabilizer." Although described as a muzzle break, by positioning of the holes, (L) or (R) will cause the muzzle to recoil (L) or (R) as in the case of Left and Right hand shooters.
I was resident gun smith for the Army when these were tested. I was also present when they were presented for Federal Law Enforcement, however, neither accepted it as a functional piece of equipment for a tactical or battle rifle.
I have attached a photo from the Military Testing files for your convenience. Possibly one of these will appear similar to what you are describing.
HJN