Strictly talking about MA law and not federal
The SOT gets you nothing under MA law
The 07 FFL gets you exactly one thing by itself, silencers. MGL chap 269 sec 10A. This is where a federal manufacturer makes you exempt from the law making silencers illegal
All the goodness comes from your MA Dealers license. Per MGL chap 140 sec 121 (very end), you are exempt from sections 122 to 129D, inclusive, and sections 131, 131A, 131B and 131E.
Some of the stuff requires MA Dealer and FFL.
There is no explicit exemption for MG outside the green card. The MA dealer exemption is a series of logical conclusions based on other laws. Since this is MA, logical conclusions that permit GUNZ are likely to be troublesome.
There is no exemption or series of logical conclusions that leads to a non MA dealer who is a 07/SOT somewhere else being allowed to possess a MG in MA. Illegal possession of a MG is a life sentence, so not something you want to take out for a test drive to see what is legal.