Good point about sanding, Will. I think this will be a take-home-and-do-in-comfort job, though. Otherwise, knowing myself, I will half-ass it. Also, there is are really nice bronze shaft that it is mounted to that I wouldn't mind polishing.
But, yeah - shrinkage. The thing is only 50 years old. I wonder if it's still under warantee.
What makes me not excited about taking it apart is the wheel is rock-solid, as it is. In fact, I fell on it this summer and messed my knee up pretty painfully, wishing that the wheel had not been quite so solid. Tells me it is not going to give up without a fight.
But, those gaps do bother me for reasons, not the least of which is the fact that they provide a great place for water to collect around the end-grain. I hadn't considered filling them. My assumed plan was that I would just replace that ring or slightly decrease its diameter (if that still looked OK). But, your suggestion gives me an idea.
Instead of trying to hide those gaps, maybe I just lean into by slightly widening them and insetting a decorative piece of contrasting wood? If I had bronze-casting skills, I could do something pretty cool ... but I do not.
Just thinking aloud and inline with your advice, perhaps the best thing to do is just start sanding with it assembled. No harm in that and it won't be wasted effort. If I get into it and decide that it really needs to come apart, I can still do that.
Re: Furniture stripping/dipping - Not a bad idea. I wonder if the bronze hub would be affected by that. Worth looking into.