I scheduled an appointment with a "Genius" at the local Apple Store, using the online webpage. I figured I'd call the store in advance to make sure I brought all needed hardware and documentation. Spoke to a dude who asked me when the WiFi access went sideways. When I replied, "Right after I uploaded iOS 6.1," he said, "We've seen this issue before. Try re-booting your Wireless Router."
I did that, and like magic, my iPhone was happily connected to my wireless network once again.
Fifty points to the Apple Genius guy for both fixing the problem AND getting me out of a trip to the mall! Five days later, and all systems are working fine.