You don't need a 3" hole bit, you need to use your flush trim bit on your router
I'm not sure that this will work. I secured plexi to the top of my panel with the trackball plate underneath. I flipped the whole thing over and grapped my router and pattern bit. The problem that I ran into is that the mounting plate is only about 1/16" wide and the cutting edge of the bit was farther away from the arbor than that. So while the arbor rode along the edge of the mounting plate, the cutting edge of the bit was too deep to cut the plexi. (See image: red = inverted CP, Black = mounting plate, Lt blue = pattern bit, Dk blue = arbor)
To fix this, I would have had to space the plexi farther away from the control panel (e.g. stick a piece of wood between the plexi and panel), but then I couldn't be sure that my plexi lined up exactly with my panel.
I ended up free-handing the router and cutting out as much of the 3" area as I could using the plate as a visual guide. What I was left with was a very rough circle-ish like hole. I then used sandpaper to sand the edge of the hole out to meet the trackball plate.
It came out great, but I'm sure there had to be an easier way.