Did a little more digging, and it appears that the Mr. Cool units are rebranded Midea ACs (there are a half dozen brands that all use Midea… this is true for microwave ovens as well).
I’m going to give this project a try, since I already have a bag of spare ESPs.
But the short version is that apparently (if the above and linked information is accurate) the USB dongle doesn’t actually talk USB… it talks 9600 baud 5v serial over the USB pins.