Turns out I had a mulberry tree growing near my apartment the whole time. While it would have been nice to have a few more mulberries for the filling, it still came out good with this recipe:
Growing up we had two large mulberry trees in the yard, and every summer I was sent out daily to pick a bucket full of mulberries. My Mom made mulberry syrup, mulberry jam, mulberry clafouti, put them in fruit salad, and, of course, made mulberry cobbler.