A registered SBR receiver without its associated short upper is, according to the NFA FAQ, NOT an NFA "firearm" so long as the owner does not have "dominion or control" over the parts necessary to turn the receiver into an SBR. In other words, you can own a registered receiver and a Title I 16"+ upper and NO short upper and the registered receiver, while still registered, is NOT an NFA item and you do NOT have to ask for permission to move it interstate. If you are permanently doing away with the SBR status they ask that you notify the NFA Branch so they can removed it from the registry, but you do not have to do so.
If, however, you maintain dominion and control over the short upper, even if its home in your gun safe while you're hunting out of state with the receiver and a Title I upper, then the receiver IS an NFA item and you have to ask for permission to move it interstate.
Therefore, an SBR registered rifle at a Class III dealer's shop is only an NFA regulated item when the "owner" (in this case the dealer) has the short upper attached and for sale. It seems to me that if the dealer is ALSO an SOT licensed gunsmith or manufacturer, the dealer can indeed modify the upper so it's legally not short and then sell you the entire rifle without going through the transfer paperwork.
You might inquire as to whether you can buy the UPPER (but not the receiver) and take it with you and have the suppressor welded on and THEN come back and buy the receiver to go with it. Without the short upper, the receiver, even though registered, ceases to be an NFA regulated item. But if you buy the receiver separate from the barrel as a Title I receiver, then buy the short barrel (or another) then you are in violation because you have the parts to assemble an unregistered SBR "in close proximity" and you "maintain dominion and control" of them.
Whether a dealer will agree to do the transaction this way is up to the dealer, but I don't see why you can't have the upper modified to be Title I-legal before buying (or simply taking possession of) the registered lower as an unregistered (or de-registered if you will) Title I lower. It would be no different from the dealer simply swapping in a Title I upper before selling it to you, although that leaves him with an orphan short upper, which might be problematic for him paperwork wise.
Of course, not being a lawyer, my advice is worth exactly what you paid for it, so ask your dealer.