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SquidPuppet, thanks. My hub is definitely the "senior" model with 36 holes -- I've repacked it several times, and just replaced one bearing cone, getting lucky with an eBay find. It was on my main bike for a long time -- a rusted heap that my college roommate found in his family's barn. Maybe 20 years ago, I noticed that one of the brake shoes was chipped, and the bike shop sold me four shoes -- each is half the size of the original shoe, and they fit into the original position exactly.
I wonder if the choice of grease plays a role. I'd hate to start a grease thread, but right now I use from a tub of marine bearing grease, and haven't thought about whether a different grease would change the braking action. On the other hand, those Shimano hubs are eminently affordable, and I might just have to get one for the sake of curiosity.
Do you know anything about the interchangeability of the cogs on the E110? I have several Sturmey Archer cogs. They don't fit on the Bendix -- slightly different diameters --, but I wonder if they would fit on the Shimano.