Sounds like you need to modify a hole cutter, which is an arm that comes off a center drill that has two adjustable cutting blade.
The modification is to shorten the center drill to where is it below the cutting edge of the blades. Put a thin sheet of plywood or something on top of the piece you want, clamp it with the plexiglass, and go to town.
https://www.amazon.com/Adjustable-Ho...s_id=256292011
[edit]
Sorry, you mentioned "fly cutter" which is probably the same thing I'm thinking of.
Frank "Why are all your tools ground down?" Giger
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