Apparently my soft reset wasn't soft enough or long enough. I had spent most of the afternoon with my laptop tethered to the Internet (cable modem). I had unplugged the Extreme and was letting it languish there without power for several hours.
When I plugged it back in - Airport Utility wasted no time in finding it and diagnosing the Internet was broken...Another quick reboot of the (cable) modem and SPROING! TexasT's is back online!
Saved me some money, that did.
Now...about that Ethernet switch...