There's a product called "Exeter paper" that's extremely similar to the backing on 120 size J&C Pro 100. It's black, opaque, matte on one side and semi-gloss on the other (put the gloss side toward the film to avoid base scratching). It comes on a roll, IIRC 48 or so inches wide, and is sold by the linear foot. It's durable enough, according to those who've used it, to be reused several times, and you can use a white paint marker or similar to put the frame numbers on the matte side. It's the recommended product for making roll backings wider than 120 (116/616, 122, 124, etc.), and though a little thicker than modern "big brand" backing paper, it's not significantly thicker than what was in use in the 1930s and a standard length roll fits nicely on original spools.

If you search for "Exeter paper" here on APUG you should fine the thread with contact information for the vendor -- unfortunately, Googling that term gives lots of hits for the Exeter Paper Company, who may in fact make the stuff but don't put much if any product information on their web site.