Being NFA doesn't completely eliminate ownership. I can go buy new DDs now, just have to file paperwork and pay $200.
I just bought a brand new, way-post-'84 NFA SBR. Hardly "strictly off limits". (Where'd you get the '84 date?)
The only thing "strictly off limits" is post-'86 machineguns. Anything else is legal with proper paperwork; if hard to get, either is a state restriction (all NFA banned in HI) or simply an inadequate market (I'd like to buy a new XM-177 howitzer, but don't see any sellers).
But yes, some DD's are off limits. Try and buy a frag grenade or HE rounds for a .50 BMG and see what I mean.
Some SBS (Short Barreled Shotguns) are DD's that you can put on a Form 4. Certain "street sweepers", or other short length shotguns, are NFA restricted and good luck getting the BATFE to sign off on your forms.
SBR's just need the right paperwork filled out, the right palms greased, and the receiver engraved.
For DD's and AOW's, it's pretty much up to the BATFE's arbitray BS whether or not they want to sign off on it.
Contrast this to my point that none of these arbitrary classifications should exist at all.
You mean the M777 towed/airlift gun that the Marines have been playing with? Neat, and under evaluation by Finland, among others, but I think the Finns are really hoping for a chance at some Swedish Archer 155 wheeled SP guns. I know a fella after one of the German 150mm guns used in the Band of Brothers TV series. I'm not sure how demilled it is, but it'd sure look neat being towed by his BTR-70....