a brake is exactly what you're looking for. there are so many good brakes on the market now, it's hard to make a recommendation. My last few ARs have gotten the FSC556 flash-hider/brake compromise. Definitely not the most effective brake, but a good bit more pleasant and since I shoot at night and with NV a lot, the FH is nice.
some of the newer brakes are more combat oriented and try to keep from throwing up too much dust when you are prone. also a nice feature, but not strictly speaking the most effective.
iirc a test i saw several years ago showed the JP recoil eliminator pictured above came in a close second for overall performance. it may not be legal in many competitions if that's what you're going for, so check the rules first, which may put restrictions on diameter and length.
people who say they're not effective on 223 just don't shoot enough to tell the difference.
i don't know for sure, but i'd think most of them would extend the muzzle at least an inch and a half to make the 16" minimum. I also don't know why you couldn't pin/weld any of them.