I think that the Luger Tips mention of Springfield barrels fitting the Luger refers to the fact that these barrels have enough "meat" on them to turn them to Luger specs... definitely not thread compatible and of course, what would you do with the 30-06 chamber that was inside the threaded portion...
No, M1903 barrels must have just enough .30 caliber barrel to make a useable Luger barrel... As the old-timer gunsmith might tell you... all you have to do is cut away everything that doesn't look like a Luger barrel...
If you want a stainless 16 inch tube you will have to make it yourself or have it made... Perhaps Orimar might make you one on special order of one of their firearms and it would come installed so you wouldn't have to worry about receiver wrenches and such... They might even cut the shoulder stock lug for you... who knows.
It doesn't hurt to ask.
The Marstar barrel isn't available in stainless and has a threaded hole in it's underside where the forearm (not of typical Luger design) is attached... not a pretty arrangement... trust me.
The FFL database as you called it is simply the 4473 forms that the dealer keeps filled out on paper... once you have "papered" an SBR, that paperwork would supercede anything prior to that in the weapon's history.