After doing some research and finding the Impossible Project, it didn't seem like such a bad idea. I started looking for old PX-70 cameras for sale. And after accumulating a small stockpile of them, I finally found one that worked.
After experimenting with different types of exposures (is it appropriate to call it film?), I found what I wanted in Polaroid's Artistic TZ. Although no longer manufactured, and long past the expiration date, I've been able find enough for sale to create a series.
Initial prints were displayed at the 2010 Cedars Open Studios tour.