How about a wind breaker in the front and polypropylene back half and wool.
I spent the better part of a day trying to track down a source for polypro to make a custom base layer, that is one difficult raw material to get. I like your idea though.
Walmart sells polypropylene t-shirts for 13$.
I have some cycling jackets that have a windbreaker in the front which is most likely nylon and a fleece back.
Combine that with a polypro shirt underneath and you should be good to go.
Brooks Equilibrium Base Shirt - Men's Galaxy base layer for 75$
That Galaxy base layer is pretty cool looking, interesting construction. The source of Polypro I was looking for, is for a roll of the material so that I can make base layers that are actually sublimated like a jersey would be. REI has some good Polypro base layers too, I have a long sleeve and sleeveless ones for various weather conditions.