Well jeez, if you want to go thru 10 times as much effort as you need to, and thoroughly enjoy overkilling things, then go right ahead.
I don't believe it to be overkill. I've had more luck drilling through plexi using a smaller bit than a 1 1/8" bit, and for me it was easier to align the CP to the Plexi. On my showcase cabinet I detailed how I cut my plexi - you can see it here:
http://forum.arcadecontrols.com/index.php?topic=55021.0But here is a quick run down -
First thing I did was clamped the CP to the plexi

Then I flipped the plexi over and drilled out a 5/8th hole. my flush trim bit was 1/2" and 5/8" bit would make a large enough hole for the flush trim bit to fit.

Drilling done! You can see the router ready to flush trim them up.

Flush trim router bit makes short work of the plexi.

I've heard of people going either direction and haven't reported any problems. You do what you think is best. I wouldn't go so far as pointing out this method as overkill or taking much more time than using a 1 1/8" drill bit. I can drill through plexi much faster with a 5/8ths than a 1 1/8th. YMMV