As mentioned already, dwell time is different. Barrel length in front of the port and the size of the port dictates dwell time and the amount of gases to operate the gun. It was previously argued by 11.5" is better than 10.5". 11.5" was more reliable in cycling the BCG because of the increase in dwell time. It made it less sensitive to a variety of ammunition. 10.5" overcame that issue by having a large .093" gas port size which is huge compared to other's ~.060"-.080". The over gassing can be felt by increase in recoil of the BCG getting hit harder, brass will be deflected forward, and more blow back gas.
But being 13.7/9", it's going to be somewhere between 10.5" to 16". I haven't heard of many running the 13" variants, but many have ran the 12.5" with no issues. Reliability should be fine since 11.5-12.5 runs fine. I have ran an LMT, and 2 different Noveske 10.5" barrels with no issues running gas port sizes between .089" and .093" with PMC, WWB, federal xm193 and m855.
Since your goal is to pin an weld, I'd honestly do the 14.5/14.7". It will give you maximum barrel length for maximum velocity while keeping it short as possible. Plenty of muzzle devices that will get you to 16" when pinned. Your muzzle device would have to be at least 2.1-2.3" longer than the muzzle to meet the minimum requirement going with a 13.7/9" bbl. I'd rather have the longer barrel instead of a bigger muzzle device.
Is really the extra length of a muzzle device really going to hinder your goals with a standard 16" barrel because you are going to at the very least have a 16" total length bbl/muzzle device? I change configurations ever so often, so I like the ability to swap things out. I would at the minimum get a .750" diameter muzzle device to have it welded on so I can still remove and install gas blocks and barrel nuts.