That is why it isn't legal for civilians to purchase without the full auto license lol.
It does not appear that you are acquainted with the ins and outs of the NFA items.
1) There's no such thing as a "full auto license." If you want to legally own a fully automatic weapon, you must have the approved ATF form with a valid tax stamp as per the 1934 NFA. This is not a license. It is a form showing you have paid a tax. There is indeed a difference.
2) Thanks to the rider tossed onto the 1986 FOPA, the full auto registry was closed in 1986. The only fully automatic firearms that can be owned by the public at large are on this registry because it is no longer legal to add things to the registry. Therefore, there's no such thing as a post-1986 fully automatic firearm on which a citizen can pay the tax. One must be an approved SOT (special occupational taxpayer) with a request to demonstrate such a firearm for sale to an approved agency in order to obtain a dealer sample, but those are not available to the general public. (There's certain rules regarding the post-86 dealer samples, but since I am not a SOT, I haven't bothered to learn them; they're irrelevant to me.)
3) The AA-12, although its design was begun in the 1970s, the current design was done about 2005. Therefore, no transferable AA-12s exist since 2005 is obviously after 1986.
Here endeth the NFA lesson (insert "the more you know" image mentally at this point
).
It sure does look like fun, but as pretty much everybody points out, it has limited utility unless you're doing rather extreme things. But it doesn't matter, since until 922o gets repealed, we can't get them anyway.