After getting my new motor with gearbox, I mounted it through a hole in a piece of wood and spent some time trying to use it, and ultimately ended up with this process:

Overall this takes about 30 minutes to make a set of buttons vs. the 90 minutes it took before. I was hoping to get it down to 10 minutes but saving an hour is still good and the process is a lot less stressful since it's so much easier to make the circular cuts now.

Old worn buttons compared to a new one (the purple one):

Some are more worn than others due to being used more. I wish the button box counted button uses, but it doesn't, so I had to estimate based on how often I think the most-used buttons are pressed and how much I play the button box, and my best guess is that the most worn buttons were pressed 300,000 times.

It turns out that the new process wasn't as easy as I imagined. The first thing I tried to do was use a box cutter that I held in my hand, but it always drifted out of place. Literally always no matter how hard I tried to keep it where I wanted it.

So I switched to the hand tool you see in the video, which worked better, but even that I had limited success with until it occurred to me to put some screws into the board (out of view in the video) that I can place the end of the tool against so that, as the button rotates, the tool can't be pushed by the spinning button and thus end up out-of-place.

Then I decided to mount the block of wood to a hinge and attach a razor blade as firmly as possible. I guess I could have done better than to screw it against some popcicle sticks wrapped in a business card but I didn't feel like 3D printing anything special. 3D printing is fun but designing shit takes forever. Anyway, this works as you can see, but only if I cut through the foil over several rotations, first just indenting it and only then slowly cutting through it.

I guess if I want to make the process faster, the thing to do would be to get a faster motor, 3D print something to hold two blades so that it makes both cuts at once, and add some kind of foot switch so that I can start and stop the motor since it's already kind of tricky to insert and remove the buttons while it is spinning.

Anyway, here's a video with bad audio that shows the new hexagonal buttons in use:

A note from the future: The original video contained a copyrighted song, so I've swapped it out with a video recorded just now which contains a public domain song. The button box actually contains the same buttons, but being 21 months later, they are kind of worn and so you can see I have trouble with some of them not responding to being pressed. It's time to make another set I guess.

I can barely even tell they're no longer round when playing it.