I played chao adventure for like the first time ever!
Well, kind of. The problem is that the VMU I was using had, in retrospect, a battery cover that was out-of-shape, causing the batteries to not be held well inside the device -- so the thing would regularly reset. Chao Adventure is basically designed to run constantly while the device has battery power, and doesn't actually save game state at any point, so I could not actually use it to train my chao.
While I recognized the clear fix for this too late -- use the battery cover from the VMU lemon that I tried but failed to get working earlier (console doesn't recognize it for some reason) which is still the right shape -- I stumbled upon a different solution that might actually be a little bit better, the VMU emulator built into Dream Explorer, a VMU-related tool that is also useful for changing icon, color, etc. without having to reset the device. It's a little clunky but works well, and you can actually use the VMU screen (though the VMU sound doesn't work, only available through the TV) to play the VMU game, and most importantly you don't need CR2032 batteries. It also saves your state to the VMU when you're done, which is nice, though I don't know why the VMU doesn't do that normally.
There's probably something lost with the minigame not running in effectively real-time, but I don't mind since this is mostly something I'm doing to bulk my chao up in order to get those race emblems. My understanding is that the predefined spots where your chao relaxes, plays with a beach ball, etc. serve as a sort of indefinite pause function for that specific purpose anyway.