Bah....a lousy 1.5" more isn't going to severely hinder your CQC experience. If anything, you will get an extra 50 yards of "frag" range out of that 223. If you could care less about the extra 50 yards of range, then even at 15 yards you still have more velocity, which will amount to more violent fragmentation, which *should* translate to more effectiveness. Hell, boys in Iraq are clearing rooms with 20" rifles. Boys in WWII did it with Garands.
If you are seriously bent on being short for maximum CQC convenience and ease, then $200, some paperwork and you can get a shorty commando barrel.
BTW, most guys are right here. Don't argue. Close a bolt on the barrel. Insert a dowel. Mark it. That is your barrel length. That is how the ATF is going to do it. And that is all that counts.