Places that won’t print stuff with logos on it are obviously not deserving of your business to begin with.
I don’t really know why you’d want to put artifacty movie caps on your stick, either, but if I did, I’d probably leave out the huge button and stick markers; If your alignment turns out to be a little off, you’re going to see those big circles underneath, and the circle around the stick will probably show when the dust guard gets moved along with the joystick.
The logo’s a personal preference, but I’d say leave out the doodads and try to print with a little bit of extra bleed on the edges. If anything, a small dot in the center of your button area should be plenty for alignment purposes. I saw the glow you put around the buttons; obviously you can leave that, but those dark gray circles probably make things harder than they need to be.
Or maybe you guys can handle putting a piece of paper on a god-damn box without fucking it up.