Yep, to my eye, it's now looking like the next size Paterson is the way to go -- just have to find a used one I can afford, with the core still in it. Taping the two films together as they feed in should prevent overlaps; I'm not sure I'd trust just pushing the first film to the center and then loading the second.

Obviously, Jobo reels would be ideal, with their little tabs that can be pushed in to separate two 120 films on the 220 reel, but they're expensive and don't fit Paterson tanks (or so I've been told). I might have to see if I can invent something like that as a modification to a Paterson or Universal reel...