Yeah you can, you just gotta pay the $$ for the permit, I think its $200. Thats how guys are making 9" 300 black out CQB rifles and what not.
FWIW, as long as the overall barrel length is 16", your "barrel" can be as long a you want.
For example, there are guys running 11.5" barrels with a 5.5" flash hider that is permanently attached. Total barrel length is 16"
I run a 14.5" barrel with a permanently attached flash hider for a total length of 16". Its perfectly legal with no tax stamp.
Yes, the most popular class 3 tax stamp is $200.