Well well well!
I was looking at my thermostat cable, and in addition to the Red, White, Green and Yellow wires that go to my existing thermostat, I noticed there was a brown and a blue wire that was cut short, but not connected to anything.
After hemming and hawing, crawled up into the attic where the furnace was, and found the brown and blue wires weren't connected to anything on that end either. I repurposed the blue wire by connecting it to the "Cc" terminal and now I have a 24 VAC common wire at the thermostat mounting point. Now I can use these new fancy thermostats like the Nest, the Lyric, or this Honeywell Z-Wave unit.
Woohoo DIY!