Gas system and barrel length are only part of the equation, as port size can have just as much, if not more of an effect, on system reliability as a whole.
The question then becomes, are those Faxon 11.5” ML barrels advertised as only working when suppressed, or only with full powered 5.56 ammo? Any user feedback you can find in regards to that question? Contacting Faxon may be the best step if you’re trying to get that answered.
Most commonly you’ll see Carbine length gas on 10.5”-12.5” barrels and as long as it has a properly sized gas port, you’ll be ok suppressed or unsuppressed (if not a little gassy). Playing with buffer weights can help, or moving to an AGB or an adjustable carrier would be better. FWIW, I’ve run numerous suppressed short barrel setups with no adjustable components in the past (primarily with barrels I had cut down and gas ports opened to my preferred specs) and they all functioned perfectly fine.
With all that said, once again depending on port size, those adjustable components may be desirable even with an 11.5” MLGS barrel, so just know going in that even small differences can add up to drastically different results when it comes to suppressed system reliability and function.