What a tempest in a teapot. Bullcrap if you'll pardon the the salty language.
Acrylic is one of the easiest synthetic materials, next to Starboard, for working with power tools. Fibrerglass, not so much because it dulls any cutting tool due to the glass content.
The challenge is that you don’t have a way to use a pilot bit….
Greg, as mentioned in post #3, use 3/4" construction (cheap) plywood as the material for a new pilot hole. The hatch frame is sitting on the work bench. Extend the pilot drill so it has a good grab before the 3-1/2" hole cutter contacts the acrylic. Attach a large piece of 3/4" ply to the underside with a few pieces of double sided tape and clamp the whole mess down on the bench. I say to use 3/4" ply so the pilot drill doesn't get sloppy towards the end of the cut. Hell, if I'm really in a hurry, I've clamped acrylic to the bench itself and drilled into the bench top for a pilot. Not very workmanlike at all

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If you cut too fast, it might melt the plastic too, so watch for that.
With every cutting tool used on acrylic, maximum speed and the lightest possible pressure is mandatory. And sharp, sharp, sharp. Carbide edges whenever possible. If the cutter is dull, it takes time, and you don't have time, you're time is valuable, time is money, so it's push, push, push, harder and harder and harder, and pretty soon the acrylic is melting, and the cutter grabs, and the cutter wobbles, and #^$&%%@$!#& what a bunch of crap

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On an expensive project like this, a brand new 3-1/2" hole saw would be in order as they don't come in carbide. If possible, on this expensive project, use a drill press.
One thing that's unfortunate about aftermarket additions like this is that "working" acrylic - cutting, drilling, machining in any way - introduces stresses into the material that can result in crazing,
There is no heat involved in working acrylic, so no internal stresses when everything returns to room temperature.
This eliminates chatter and other problems, especially with thin acrylics.
If this is a Bomar or Lewmar hatch, it's at least 8mm (0.315") thick so no worries there.
All of the problems quoted above are due to operator error. If you're using a electric hand drill, practice, practice, practice on scrap acrylic before digging in. Start twisting and wobbling and it's game over.

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