And just to prove that I'm not just making up stories about repairing hundred-year-old furniture for the page hits, here's a picture of the repaired table, with the fixed caster in the center.
The table has a pedestal base that splits in the middle; each side of the base has three casters, and a central post with a caster supports the table when it's pulled out to its largest size. Here, you can see two of the original casters as well one the repaired one.
My wife mentioned this weekend that she'd always been really frustrated by the broken caster, but never had the stamina to complain to the refinisher and get him to find a replacement of the correct size. She was ecstatic that we could fix the table, and even happier that we'd learned some new techniques to make the replacement part.
Once again, thanks to Shapeways for the replacement part, and Makerbot for making me trust that I could make a correctly-sized replacement part!