Glad I live somewhere that has actual seasons instead of summer, more summer, and still summer.
The old county sheriff here only wanted the same paperwork as a CCW application, and 4 extra personal references (so 6 total). If you already have a CCW, he just wanted 4 more references. From what I heard from everyone he called, he mainly wanted to make sure I wasn't an alcoholic or a wifebeater, other than the usual character reference stuff.
We just got a new sheriff a couple months ago, though. One of his campaign promises was that he wasn't going to make it any harder to get an NFA signoff (both candidates promised that, actually). I've yet to hear if he's lived up to it, but a
lot of people are going to be
real mad if he doesn't!
Personally, I'd rather go the signoff route, because most local and county cops should recognize the sheriff's signature. Without that, the Form 4 is just this weird piece of paper they've never seen before. With the signature, it's a weird piece of paper that the county sheriff signed saying that, to the best of his knowledge, it's legal for me to have this thing.