Is it a problem that my post bases overhang the footing edge slightly?
If I understand correctly that the post bases overhang the sides of the concrete piers slightly, it's not an issue. As you said, 6x6 posts are unnecessarily large for the load, so as long as you have the equivalent of a 4x4 resting on the concrete it's all fine.
Just use caution when drilling for the post bases so you don't spall out the corners of the concrete. Skip any fasteners that are too close to the edge and put in extras elsewhere if possible.