You could get a 14.5 inch pencil barrel, get a Bushmaster "slip over flash hider, which I believe has about 1.5 inch in front of the threaded portion, and pin it on. I had a 16 inch with a slip over, and it was too long. 16 inch gives you about 3100-3150 fps with 55 grain, but the 14.5 ives you 2900 fps and 11.5 gives you about 2750. It takes 2550 to 2600 fps for the USGI M193 to fragment and tumble effectively. That is why i went with the 16 inch M4 barrel on my carbine build.
Here is a build I did for my son about 4 yeras ago, though he later went with a birdcage FH.