Wow, way to make friends and impress others. Nobody here will give you any grief for building a short barreled 308, so you don't need to leap right outta the gate in full a$shole mode. You can leave that for another place.
As far as gas system length - that depends on how short you go on your barrel. You'll have a hard time running carbine gas on an 8" barrel, if you end up there. Gas system will mostly be determined by what barrel you get, and where that barrel manufacturer places the gas port. You have little choice in the matter, besides picking your barrel and running with it, unless you're making your own barrel by your own hands.
I built a 13.5" 308, and it runs like a champ. I put a 2 3/4" brake on it, so it's not a papered-SBR.
This guy built an 8" short barreled 338 Federal SBR: