I just drilled my plexi this past weekend. I glued my hole pattern to it, clamped it to my c/p board, and used a 1 1/8" hole saw to drill. Never had a problem at all. I started with a (small) drill press but I couldn't get most of the holes because it wasn't big enough to reach towards the inside of my panel. Put the still clamped panel in a vice with a couple scrap wood blocks in front of the jaws and drilled with a power drill and the hole saw.
I wish I had a forstner bit, the hole saw would load up with the cores and I would have to remove them every time I drilled.