The recipe was basically this, but with double the flour (I didn't use self rising) and probably thrice the fruit.
It's such a simple recipe, it's easy to customize to taste. If you're using a sweeter fruit, cut back on the sugar in the batter.
I wouldn't think that those would be too moist. Peach cobbler is pretty good. Most of the juices will have enough time to cook down, and the remainder will work their way into the batter.
I also just realized that I used blueberries, not blackberry. I made it at the inlaws', and mindlessly tossed in the bowl of fruit they'd set aside for the cobbler.