On further examination, I don't think that adapter will work for me. I think the relevant measurement is the diameter of the bottom bracket. I have bike with an old, one-piece crank, and it's BB has a much wider diameter. The BB I'd like to replace appears to be 4 cm or 1 + 5/8 inches in diameter, but I don't see where that measurement is tracked on any conversion unit.
Basically I'm at the point now where the big obstacle in the restore is my needing to decide if those pressed in cups come out (or if they even can come out) or if they stay in. Is it possible to modernize this in any way? I would at least like to ditch the cottered cranks, because I'm guessing they will be a pain to find replacement parts for, but really I'm just overwhelmed by the volume of bottom bracket info available, and by how I can't figure out how determine if any of that info applies to my current situation.