So if I wanted an AR made into a full auto, there's no legal way of making it happen?
Yes and no.
You can find what is called a "lightning link" that was registered prior to May 1986. It will convert your AR into a machine gun. I haven't priced them in a while but they should be upwards of 7 or 8 thousand dollars.
SWD Lightning Link
The other way to do it is to buy a registered Drop In Auto Sear (RDIAS).
Drop In Auto Sear
More expensive, but more durable and robust.