Alanint is right about the CLEO signature being a problem in many places. I was hesitant to bore everybody by going into non-Luger detail on that one. A few years back, the firearms prohibitionists added this minor roadblock to the law, in an obvious attempt to give regional anti-gun politician cops an arbitrary tool to sandbag law abiding would-be Class III purchasers even in states permitting it.
The good people of one state, Tennessee or Kentucky as I recall, fixed that by passing another law saying the chief law enforcement official WILL sign the form unless he has specific reason why the purchase should be blocked.
And if you run into one of these politician cops, you have lots of alternatives besides going the corporation or trust route. If you live in town, you may first go to the chief of police. If he balks, you are allowed to go to the next level, which is EITHER your county sheriff or a judge. If they give you the bums rush, you can eventually go to the state attorney general. I.e., you work your way up through the CLEO chain of command, so to speak. Few have to carry it that far.
It's a bit difficult for a local or state official to explain why a law abiding adult citizen who can pass a rigid FBI investigation cannot be trusted to own a restricted firearm or controlled item such as a sound suppressor. Years ago I was idly talking with some ATF people in the metropolitan Washington area, when I lived and worked there. They openly scoffed at some of this prohibitionist legislation, which merely clogs up their system; most of them are gun people, too. They said they never ever have problems with people who make the effort to follow the rules. Why harrass them?
...which is what we all know and say to each other.
(Matter of fact, the time of that discussion was when I was moving out of the D.C. area, back to hometown Ohio, and there was an hours long delay at ATF headquarters, where I needed to get an interstate transport permit for a couple machineguns signed. Seems they had lost all the registration paperwork, and the hunt took a long time. ...which, it turns out, was quite common in the '80s and early '90s, before computerized records systems were instituted and debugged.)