I used a dremel tool to route out the hole from 1 1/8" to 1.5 ". I don't think I can recommend this since now I do have some rough spots after I assembled the joysticks and for the time being I am just going to live with since I don't want to take this apart again. The rough spots aren't that bad but you will notice them if you move the joystick around in circles, but for most games you would never notice.
Cutting that plexi is going to be tough. I think the only way to do this would be with a dremel tool and do it slowly.
Keep in mind these sticks do have a larger throw, but you don't need to move the joystick the whole distance, so if you hit the wood with a smaller hole you might be OK. Try it and see how it feels, but I think you should at least go 1.5"
One other thing I noticed is the dust cover sometimes hits the hole. It doesn't get stuck, it just makes a snap noise. This has only happened a few times.