Okay, mebbe I burned out too many brain cells this past weekend taking those tests. Or maybe I've been pretty dim all along.
I'd bought one of the original LinkSys BEFSX41's (old enough not to have a "version") for my home network. Somewhere along the line, it started acting up, dropping the internal connection and refusing to talk to my computer. Tonight I accidently left my only other router at school and was forced to try the LinkSys again. POS dropped out after 10 minutes and then wouldn't stay up for more than a minute or two if I left it connected to the cable provider.
So... after unplugging the provider and rebooting the router, I went through each menu option, examing ALL of the settings. Damned if I didn't find both options for UPnP turned on. Since then I've been online for over 30 minutes.
I'm keeping my fingers crossed and hoping it'll still be working in the morning. If my wife discovers that she's going to have to spend the day offline because of "no router", there'll be hell to pay.