Woo! After fussing with this for a few days, I have finally had success making frozen yogurt. Today I had the strained and flavored yogurt all ready and put it in the frozen ice cream maker drum while the drum was already spinning. 20 minutes later I had perfectly smooth, creamy, completely fat-free frozen yogurt.
I adapted the recipe below from a few different sources.
Vanilla Frozen Yogurt
3 cups strained yogurt, I used fat-free Fage Greek Yogurt
3/4 cups white sugar
1 T vanilla extract
To make the strained yogurt, line a mesh strainer with a few layers of cheese cloth and fill with 6 cups of yogurt. Cover the yogurt and place strainer in a large bowl, refrigerate for 4-8 hours or until all liquid has drained out of your yogurt.
Mix sugar and vanilla in and allow sugar to dissolve completely, about 30 minutes.
Pour into prepared and running ice cream maker and let run for 20-30 minutes.