The answer appears to be: use the dishwasher. The water doesn't get recirculated in such a way that you will contaminate the egg, the jets are strong enough to blast off the yuck, but not strong enough to break the eggs. Dried fifteen egs with paper towels after a rinse cycle and they looked as good as my best results with hand-washing--and a lot less mess, work, and frustration.

Apparently if you get into the thousands of eggs what you do is buy a machine that washes, dries, "candles," and in some cases grades the eggs...The super-expensive ones even pack and wrap the eggs in filler flats for you. Zoiks. I don't think we'll ever get in that neighborhood. A little trip through the rinse cycle works for me.