A SIG 556 SBR will allow a true side folding stock instead of the AR collapsible. If that matters to you, an AR SBR will still have the buffer extension sticking out the back (unless you go with the late Para or new RRA side folders) and be longer than a 556.
If you go AR, you might also consider a factory SBR. No engraving required, same tax $ and time as a pistol or rifle conversion. Of course, you couldn't take it home until the paperwork clears; so if you want to play with a AR rifle or pistol in the meantime this wouldn't work.