Are you using a flash unit or anything? I only print shirts w/ oils, but I know Speedball sells some waterbased fabric ink. I watched a kid do it once, and you could even do multiple colors (with if you wrapped each shirt around some cardboard so it wouldn't budge at all). When he did it, he just did like one of two pussy hits on the screen, the shirt moved.. ect. So it looks bad. BUT, the shirt also really sucked, so I dunno. He wrapped the shirt around some cardboard. If you want to do it good, I suggest getting a flash unit or hairdryer and drying the prints, then hitting them again and applying a thicker coat of ink. I'm sure they would look really good if you did this. Also, it wouldn't hurt to dry them all and take them to a local t-shirt shop and ask to use their belt dryer to cure the shirts. So yeah, try speedball, it might be acrylic. I don't know what you would put in water based though. I wouldn't print with water based anything if it would ever get washed.
By Unidye I'm assuming that you mean Union's ink. It's a very strange ink because it smells like oil base but it cleans up with water. I'd get the retarder that Union makes. Unidye is a pretty creamy ink. I really like the way it sits. Be sure to catalyze it.
I like the way GB just babbled about nothing relevant, he was up way past his bed time.