Thought I'd post this in case anyone else has the same issue, because the fix is not obvious and I just happened to find it.
If you get funky smooth shading on the main surface of the console around the buttons, and you've already checked that all the vertices that make up (surround) that surface are flat (e.g. scale > Z > 0), then try lowering (-Z) the indent loops for the buttons. In other words, the edges around the buttons that are the lowest down.
Lowering all these indent loops for all my buttons just a tiny bit completely fixed the shading issues.
(Posting this with images didn't work (400 error) so hopefully I explained well enough)