BBl's are no problem. I suggest an 11.5 for a short one . This way once you get the stamp approval for your suppressor [ yes you'll have one sooner than later] it should run with little if any issues. I have not had any on the 11.5's i run. Most suppressor mfg suggest a 11.5 to avoid "potential" issues as they might happen on shorter ones. I know a few running supressed 10" uppers.
Upon you FRIEND getting approved, IF he cannot locate a bbl have Burt cut, thread and recrown one.
Remember Look for solutions, Not Problems.