So, possible change of plans.
The lazy bones in me is possibly taking over- I found a complete 3 speed fixed gear hub/wheel/shifter on eBay for $250. It's 700c which means I'll need to get a 700c front wheel too, but since it's fixed gear, I'd only use a front brake; I've never come into problems with a front brake stopping a 700C wheel on a frame built for 27" wheels, even though some say you don't brake as well.
I already have a fixed gear in the stable, and the idea of a 3spd fixed gear makes me a little giddy. I don't know why I didn't consider this from the get-go. Probably because I was just in northern Italy where everyone rides around on regular 3 speeds going "Ciao" and wanted to be just as laid-back as them.