I don't have any specific loads worked up, but a relatively fast-burning rifle powder like IMR 3031 might be the way to go. You don't mention what projectile weight you desire, but I would expect 3031 to give you decent velocity up to 165 grains, perhaps heavier. Another possibility is AA# 2015, which should meter through a powder measure somewhat easier.
You might inquire of powder manufacturers for suggestions. I think there are a few powders available that may have flash suppressants in their formulation. I'd make a decision on what projectile weight you want, first.
Another consideration is whether a particular powder is too fast-burning or slow-burning to work well in the action of semi-autos. Garands are somewhat famous for needing powders with burn rates in a fairly narrow range. Later designs, especially the ones with adjustable gas regulators are somewhat more forgiving in this respect. I'd be surprised to find that 3031 is too fast burning to work in a modern semi-auto, but AA#2015 might be.
Hodgdon H335 was formulated to burn a 25.0gr. charge completely in a 20" barrel behind a 55gr. .224" FMJBT projectile. A .308" barrel of equal volume would be @ 10.6" long, but the powder charge for a 150gr. .308 load using H335 is larger by a factor of 1.7. Your 16" barrel is longer by a factor of 1.5, which may be close enough to 1.7 to give H335 a try.
This is an extremely rough approximation I'm making, and is complicated by projectile weights differing by a factor of 2.7 to 3.0. But the algebra involved suggests to me that rifle powders with burning rates between 3031 and H335 may be the most likely to burn completely in a short .30 caliber tube.
Ultimately, it's going to come down to trying various powders and finding out, but perhaps I've narrowed the search for you.
Hodgdon Benchmark is faster burning (depending on the burn-rate chart) than H335, and may be worth trying. Alliant Reloader 10X (if you can find it) might also work.