Mr. Miller did not bring this case to the U.S. Supreme Court. The U.S. Attorney did.
Second, the U.S. Supreme Court case was whether the 1934 NFA violated the second amendment -- ie., if the tax stamp on the weapon was an infringement. At this point, Mr. Miller was irrelevent.
"IMHO, if you had a Miller-type case today with an M-16 or an M-4 at issue"
That's too easy. What if you had a Miller-type case today with a sawed-off shotgun with a 10" barrel?