You could also try if your buddy buddy with the sheriff to deputize you and allow you to purchase the weapon. Out here that isn't that far fetched and still is considered legal unless you lose the "badge". I found this out from a guy who didn't want to pay like 15K plus for an MP5 and found out if he did it that way it would have been just something like 2K. Can't verify, but just like certain body armor, if you can get an leo or mil to sign off on it, you can buy it.
Negative. Full stop. Halt.
It is NOT now, nor has it EVER been (since the closing of the NFA register) legal to do as you suggest, ANYWHERE, here in the United States.
Can an individual LEO purchase a fully automatic firearm? Yes, without a doubt. HOWEVER, they still have to jump through ALL the hoops that a non-LEO would have to. This includes FULL compliance with all applicable Federal, State and local laws. As an example, I live in WA State--which means that I cannot legally own full auto, SBS/SBR or AOW, EVEN as a police officer for private use.
Can an individual LEO purchase a full-auto as a DUTY gun? Yes--and it CAN be of recent manufacture, and of any current model.
HOWEVER...
The firearm will be NON-TRANSFERABLE. The firearm MUST be purchased on Department letterhead, with the Chief's signature, and MUST be used as a duty weapon. Here's the important part...
WHEN the officer leaves the Department, the FA firearm MUST REMAIN WITH THE DEPARTMENT, unless the officer is rehired by another Department, AND they agree to a transfer of custody between Departments.
If the LEO leaves the law enforcement profession--as in fully sworn police officer, THEY LOSE THE FIREARM, WITHOUT HOPE OF COMPENSATION OR REIMBURSEMENT.
Even though this is legal, I have NEVER heard of ANY Department in the United States approving the private purchase of a full auto firearm by an individual officer for duty use.
As far as being "buddy buddy" with the Sheriff, and having them "deputize" you for this purpose, there are so many things ethically wrong--and ILLEGAL--about that statement that I won't even comment on them.