Model 12...
Not entirely true.
The first mass produced wood pulp paper mills opened in the United States in the 1840s, and by the time of the Civil War they were supplying increasing amounts of paper in the United States, including for use in cartridges.
Traditional cartridge paper was, as you say, linen/cotton based, but with the enormous demand for cartridges during the war that quickly went by the wayside because it was far more time consuming and expensive to produce.
The British were using machine formed pulp paper tubes for Enfield cartridges prior to the Civil War, partially as a means of automating as much of the cartridge production process as possible.
Here's a nifty little paper on the subject that I found some months ago:
http://www.newyorkcivilwar.com/qm/cartridgetubes.pdf
No, modern "cartridge paper" isn't like the old cartridge paper, but old cartridge paper wasn't like the older cartridge paper, either.
I have no doubt that with some experimentation one could make credible Smith cartridges using modern pulp paper.
One of these days, depending on how bored I get, I may just give it a try.
"Smith carbine paper cartridges were much thicker, more like paperboard. Think of a paper shotgun shell, and also were foil-lined. This was to contain the actual pressure of firing, something the rifled musket cartridge paper wasn't used for."
I don't have an original Smith paper cartridge, and I'm not going to spring for one, either, just so I can dissect it, but it's my understanding that the thickness was built up through multiple rolled layers of heavy cartridge-style paper.
I've never heard of any of them being machine formed from pulp as the Enfield cartridges described in the link above.
I also don't believe that all of them were foil lined. There were multiple manufacturers of Smith cartridges. Some makers apparently shellacked the insides of the tubes to waterproof them.
The largest maker, Poultney and Trimble, did produce foil lined cartridges, not only for the Smith, but also the Galager and other carbines that used a built up cartridge.