Ask...

... and ye shall receive an Ultegra bottom bracket free of charge. It's used, but with a thorough cleaning and bearing repacking, it feels and looks like new. Beats buying a new one, and I got to see the actual ball bearings, so I could visually verify that the bearings are at least in serviceable shape. (One cannot tell by visual inspection if bearings are in excellent shape, only that they are or aren't serviceable)

Bike feels amazing compared to before (pedals roll easily now), and I can't wait to try it out. The side play is gone, too. Maybe that'll help with my front derailleur adjustment issues. The old bottom bracket had failed seals, and the bearings were nearing failure. The whole thing was a mess, and it's no wonder it felt like crap.

On a note of saving money:
I noticed during the process that the bearings can be replaced. I think in the future I will try to replace just the bearings instead of the whole bottom bracket. Also, the new one was given to me by a customer of the bike shop I visit from time to time. I'm still at that shop. Johnny, the Brazilian man who owns the place, installed it for me, so I'm interested to see how much this free bottom bracket will cost me.

I would like to have installed it myself, but learning is fun, too.