OK, here's a quick update...

Since I didn't have a drill press and wire wheel like the one displayed above by JDT, I decided to do a head to head comparison between liquid Dawn (grease-cutting) detergent and carb cleaner. I would have tried a citrus cleaner as well, but the only thing citrusy in the house was lemon pledge (it does great on the wood furniture, but probably wouldn't have worked as well on a goopy BB cup).

I mixed the liquid Dawn fairly strong with water and dropped a BB cup and headset cup into the mixture to sit over night. The water was definitely MUCH dirtier this morning and the goop in the cups did wipe out for the most part but it was tough to remove it and there were still small vestiges of the crud in the spots that were tough to get to.

After this, I took the carb cleaner to the remaining two cups and gave each one a good spraying and let them sit about 5 minutes. The gunk wiped right out! I then finished the bearings, BB spindle, and the two cups that were in the liquid Dawn with the carb cleaner. They cleaned up perfectly as well.

As much as I would prefer a greener approach to cleaning out old, gooped up grease from parts, the carb cleaner is tough to beat.

Thanks again for all of the suggestions!

Texbike