Here's how I did it with some pictures to show:
I clamped my 1/8" plexi over my control panel with the holes already drilled in the wood. I did the cut to size of the outside edges with a router and a flush trim bit. The bit cut threw the plexi just like a knife through warm butter. Basically felt like I was melting it to the right size. Really quick through and an easy cut.

For the button holes, I went really slow, especially working with a forstner bit which I thought was probably not the correct bit for plexi. Something with a much sharper point I think would have worked better. Sharper and a very steep profile.

Some cuts were a bit too close together, and I was worried about getting a crack between the two spots. So I started putting the buttons in to help hold down the plexi and keep the work supported.

If I pressed a bit too hard while drilling and tried to go a bit too quickly, I did get cracks inside the area that was being drilled out. Luckily, I think I got through the whole thing without causing it to shatter. Like the others guys said, I think the trick is high speed with the drill, very slow speed through the material.
Finished holes:

Seperate peices, good view of joystick and trackball cuts here:

When drilling holes for the joysticks and trackball opening I moved the plexi around and used the button holes for better support. If I had done it where the joysticks openings were, it would have been a disaster.
The trackball starter hole, and center joystick behind it (where the 4 way stick will go):
I used the trackball mount as a template for the router to make the hole the correct size. The metal here is
maybe a 1/16th of an inch. I was extremely careful that I lined up the flush trim bit at the exact right depth to make sure the bearing made contact with the metal.
Finished up:

Here's the peices seperated but now with the final holes cut.
