We switched the wireless authentication and encryption over from WEP to WPA2-PSK (good, and easier to configure) with AES (much better encryption).
Everything is working like a champ.
Well, except for some reason both laptops choke when the wireless router is set to 802.11g-only mode. They'll only connect when it's running in mixed (b/g) mode. The wireless bridge doesn't have any problem in g-only mode. Very strange.