Did they come from the same source? Maybe the former owner just decided to paint them all.
Have you checked the Griswold and Wagner sites to see if those bases were ever japanned? eBay might be another source of info, although you might have to really search to find out anything of value.
I own a Griswold waffler but it does not have a base, painted or otherwise. I also own a Belgian cookie iron that does have its base. It's seasoned like any other cast iron cookware, but it's not Wagner or Griswold.
It sounds like the paint needs to be stripped regardless, so I don't see any reason you couldn't strip it and season it. If you check eBay you may be able to see if any of the listings show bases with the japanning. The only ones I've ever seen were seasoned, so who would know what the original finish was on yours? Are you likely to replace the original finish with new japanning even if that's what it is? If not, then it doesn't really matter whether the bases are japanned or not.
You could also check with antique dealers and Griswold collectors. Someone will know if they've seen pieces like yours with a japanned finish, and/or if such pieces were ever produced. That might be your best bet, especially if you could take your pieces to them to examine in person.