It was Japanophile (not sure whether Otaku or Weeaboo applies) Joey Lindsey who alerted me to the overlap between the gumball machine and gachapon.
I had never heard of it, but I liked gachapon as soon as I started reading about it: a universe of vending machine-dispensed toys popular in Japan.
Surprisingly, the name isn't Japanese: it's onomatopoeic, a combination of the "gacha" sound the hand crank makes, and the "pon" of the toy capsule landing in the collection tray.
The overlap also highlights a common feature: neither gachapon nor the gumball machine is about candy in general, or gumballs in particular. Both dispense capsules, although the gachapon capsules are generally bigger.
Here are three good articles on the gachapon phenomenon:
Julia Hansen, the manager of Fab@CIC, an avid student of languages and culture, appreciated the distinction right away.
All cultural issues aside, gachapon is just a more accurate description of the gumball machine.
So from now on: it's gachapon, or a common English translation: "capsule toy machine."
It's going to take awhile, and don't expect a smooth, consistent transition, but I'm hoping that "gachapon" name will have a subtle, positive, influence on the project.