So I did, in fact, do more work on the PoC interface and need some feedback on the menu buttons:
Text buttons:

My first draft, just whipped up for placement, but clear.
Image buttons 1:

My second draft, with Menu left as text because I couldn't think of a good image.
Image buttons 2:

With something for the Menu button, but I fear for clarity.
Sidebar 1:

My first attempt at a sidebar to help the menu buttons match the arrow buttons.
Sidebar 2:

Because I was afraid there was too much yellow.
Sidebar 2b:

Just a pixel out further, which makes it match the width of the gems and gives equal width on all sides.
Sidebar 2c:

Made smaller instead of larger.
Sidebar 3:

Because I happened to be messing with the layers and it worked well.
Sidebar 3b:

Sidebar 3 with sidebar 2b on top instead of sidebar 2.
Sidebar 4:

Because maybe a lozenge would work to break up the yellow a bit?
Which set of buttons is best? Which sidebar looks best? Is a sidebar even needed?