What Kari said but you can drill out with a hole saw that fits into a hand drill your right sized hole in 3/4" ply and then secure to the plexi with clamps. An extra piece of ply on the other side is a good idea for rigidity and strength. I would also remove the pilot drill. The ply is deep enough that you won't have trouble re drilling the smaller hole. The only caution would be to insert your hole saw and then just before contact with the plexi start the drill slowly and you should be fine. Routers are good but it's an extra tool that you have to get if you don't have one.
I hope this helps and that it made sense too. I also like Kari's idea about the beer
