Blueberry-thyme frozen yogurt that is almost awesome

The new HEB had blueberries at an amazing 97 cents a pint last week, so we bought three of them. I had been wanting to try to make frozen yogurt, and I thought blueberry would be a good flavor for that. I didn't want to use any sugar, so I decided to add an herb flavor to make it a little more sophisticated. A quick taste test on the balcony showed that thyme was the right herb for blueberries.
I think I've gotten a little cocky lately. Most of my recent culinary experiments have been smashing successes (chickpea flour crackers, red pepper-tangelo sherbet, eggplant basil, oversalted kasha stirred into scrambled eggs, etc.), so I decided I didn't need no stinkin' recipe or any guidelines for making frozen yogurt. I made up a recipe, using just a tiny bit of sugar, and froze it. Unfortunately, it didn't freeze very well in my little ice cream maker, so I had to put it in the freezer for a while, take it out and crank it, etc. After eating dinner, we dug into the yogurt, and it was great. It was pleasantly tart, the blueberry flavor was rich, and the periodic bursts of thyme flavor were lovely. Next time I might steep the thyme in simple syrup to increase both the sweetness and the thymey-ness, but overall it was very nice. After we ate our dessert, we froze the rest like we usually do.
Unfortunately yesterday when I got it out to have some, it was as hard as a rock. I'm sure it would have softened in time, but I had to leave again before it was soft enough to eat. I was able to scrape a few spoonfuls off the top, and they were quite tasty, but I couldn't get very much. I have some theories on what went wrong and how I might fix it next time.

1) I didn't use much added sugar or fat, which lower the freezing point, so the mixture is too much like ice. To fix this I can add more sugar and maybe some cream next time, or use thicker yogurt, which has more fat and less water.
2) The way I froze it, taking it in and out of the freezer, didn't incorporate enough air into the mixture, so it froze too solidly. To fix this, I can make sure the freezer isn't too full and the little cannister that's supposed to go in there gets cold enough. I can also try to whirl it in the food processor and see if that breaks it up and adds some more air.

Have any of you had this problem, or do you know more about frozen dessert science than I do? Any tips would be welcome.

Blueberry-thyme frozen yogurt
1 1/3 cups fresh blueberries, rinsed
2 tbsp fresh thyme leaves, thick stems removed
1 tsp sugar
About 1 cup plain yogurt

Puree blueberry, thyme, and sugar. Pour into 2-cup measuring cup and add enough yogurt to equal 2 cups total. Mix thoroughly. Freeze in ice cream maker according to manufacturer's instructions.