Okay I updated my drivers and got it to launch and played a while. As expected, my Phenom II X4 and R9 270X aren't the best at playing a brand spanking new game. Here is what is working for me:
The biggest thing for performance was to set Max PPF to 16. Screen space reflections doesn't seem to change performance much, and I can't even see what it changes anyway. The unfortunate thing is how weird the performance difference is when changing "Additional Quality Settings" since it is perfectly playable at Ultra, and looks way better, but it's just an inconsistent framerate that drives me bonkers. For a much closer to solid 60 (still wavers to 55) I have to set it to Medium, which looks significantly worse. I'm not sure the tradeoff is worth it.
Hopefully AMD will release one of those "increases performance in this specific game by 40%" driver updates. It doesn't look much better than Rage, which runs like a dream, so I think it is likely we will see such an update.