I left them to firm up overnight, and then put them in the fridge so they'd slice easily.
I sliced the canes into 3/8 in. slices, and pressed them lightly between 2 pieces of parchment paper with slight pressure from my thumb. This rounded the edges off nicely and made them very button-y.
You can see the 2 bamboo skewers (taped together) that I used to start the holes. They're easy to position when they're taped together. I ended up with 8 buttons that would be perfect for my sweater, and 3 that are slightly larger. Those will be for a future project, since I still have lots of the same willow green yarn.
I even got daring and rolled out a square-ish cane. That one produced some really interesting buttons that are about 5/8 inches in diameter.