I source most of our ammunition from North Sylva so if you have a local dealer (including all Crappy Tire stores that sell ammo), that buys from them you can get some 16 gauge.
Just a quick check shows that they have 2 3/4" #4, 6 and 7 1/2 lead, #2 steel, a few options for slugs, #6 Bismuth and #1 Buck currently in stock (mixed suppliers - Federal, Winchester, some Remington). We keep a "bit" on 16 gauge in the showcase but it's all about "what sells" when it comes to what we carry. But as others have stated, mostly you just have to ask.