After rereading my post from yesterday, I realized I could answer my own question and figure out a way to stop crying.
Wearing ski goggles provides more funny stories than actual relief from irritation. (True story: I once came home to a late-night cooking session in which a drunk roommate had ski goggles on while chopping onions for a quesadilla. Hilarity ensued.) Goggles don't work very well because the sulfur product released by chopping still lands in your nose and attacks nasal nerve endings.
The solution Harold McGee offers in our useful textbook, "On Food and Cooking: The Science and Lore of the Kitchen," is to minimize the excretion of the sulfur product in the first place.
Soak your unpeeled onions first in ice water for 30-60 minutes. The cold water will minimize the release of the tear-producing sulfur. Then when you go to cut your onion, these acidic molecules won't reach your nose and eyes.
Goggles: good for sunny days on the hill, not so good in the kitchen.