Turns out that F4 came today. When I went to pick it up I asked, dealer resisted, and I found the block (22 or 23 I believe) that says NFA items exempt from NCIS check. Then the guy flipped to the back and the instructions for that question said that the NICS check can be skipped if proper documentation can be provided by some US code.
Frustrating, but it's good info to know. Next time, I'll have looked it up before going in.