Not completely correct...
"Once its registered as a SBR though, there is no minimum."
That's not necessarily true. The Form 1 includes a space for length of bbl and overall length.
If the manufacturer is smart they will put "less than 16 inches", but I have seen some that said things like "10-14" inches. In that case, you can't go less than 10 inches even after the tax stamp is received.
If you build one, be careful with the wording.