he is trying to cut the plexi after the fact to match the CP. This probably means that the exisitng "hole" is a cut out square for the mounting plate.
Yikes, hopefully that's not the case.
I don't know that all is lost if the hole in the wood has been cut away though.
What about trying this:
Secure the mounting plate to the particle board in it's final position.
Clamp the plexi to the board in it's final position
Use the hole saw to cut a hole in a separate thin sheet MDF.
Remove the resulting disc from the barrel of the saw carefully without enlarging the hole the drill portion of the saw left in the center of the disc.
With both the particle board and plastic still clamped together, turn the panel upside down so the plexi is on the bottom and you can access the mounting plate
Remove the saw barrel from the hole saw, so only the drill portion remains.
Center the MDF disc in the hole of the mounting plate. You'll probably have 1/8" or so around it.
Hold the disc CAREFULLY and firmly in place and place the drill back through the hole it originally left in the disc. Remember... the saw barrel is OFF the drill and arbor at this point

Drill through the plastic carefully so you leave a perfect hole taking care not to enlarge it or allow for slop.
Unclamp the plastic from the particle board.
Replace the saw barrel onto it's arbor.
Feed the drill back into the small center hole you just made.
Drill the 3" hole using the small hole as a guide.
I imagine it will align about as accurately as you aligned the disc within the hole of the plate.
Or maybe I'm just talkin crazy talk.
To bullnose the plexi you would simply cut another 3" hole in a scrap piece of wood, align it with the plexi and clamp them together. Then use the hole in the wood as a guide for the router bearing.