I can't say if this s.o.p. for DE / Sega games or not, but I think 1 standard size increase would work. When drilling the plastic, go slow and easy as to not let the drill grab and pull through the hole to quickly thus cracking or breaking it.

I've enlarged holes before with no problem with this and I'm talking BIG enlargements and it works great with no wood backing. These pictures are of the enlarging of the pop caps of my Avatar for the mini domes to be added. Didn't crack or chip any of them and I didn't even have to sand the holes when I was done.

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Make sure your plastics are flat. The hole, if it just wiggle room you need, could also be made larger with a small file.

That's called a 'step-drill'. Yes, the way paul is using it, the hole will self center in an existing hole. Looks like it works pretty good.

I use that type of but at work all the time. We call it a unibit. The brand name ones can be $50+. I've been buying the Harbor Freight ones for around $15, I think you get 2 in the kit. It's help up pretty well in commercial construction. I wouldn't recommend holding the part with your bare hands though, even with plastic. I've seen some pretty bad injuries with a drill turning something into a circular saw when it catches.

As mentioned above flatten the plastics also, just put them back down on a cookie sheet and use the oven at about 200 degrees for a few minutes. Be sure to watch them and as they just begin to flatten take them out. Works great.

Yup self centers perfectly and I had no problem holding the plastic and moving it upward slowly. The drill press was on a slow speed.