Finally, I cut out the thin material between the two main compartments. The "main" compartment's zipper is just too shallow to offer much utility, and the second compartment is too small. So I fixed it by just creating one compartment. I settled the frame into the bag, and there we go. It fits 6 in the frame and 1 in the putter pocket. There is potential for more disc space, but I need to tinker some more.
On the plus side, it stands up solid with no more risk of falling over than any other bag.