So I wasn't just being crazy thinking that yixing gaiwans won't work. I read about how yixing teapots should not be used for greens and whites since it insulates heat better, and can kill the delicate flavor of the teas. Then I saw on a site that there are yixing gaiwans, and thought that it kind of defeated the purpose of a gaiwan.
One good thing about a gaiwan, even a yixing one, is that they have large lids. By positioning the lid to let heat out, you can control the amount of heat retained. Using the lid this way, along with carefully controlling the temperature of the water you add to the leaves, allows you to brew more sensitive leaves like white and green.
I tend to like yixing gaiwans because they are quieter when you slide the lid along the cup as you stir the leaves during brewing. Instead of the high pitched clink you get from porcelain, yixing gives you a pleasant and quiet scraping noise.