OK... I reburned the Leonardo bootloader for a second time, which cured the constant blue-screens on the PC. Then I reconnected the board, uninstalled the board via the Device Manager, reconnected the board a second time, and now it works. Huh???
I didn't even install any driver for it. Windows shows that it's using C:\Windows\system32\DRIVERS\usbser.sys as the driver. And instead of showing "Arduino Leonardo bootloader" in the Device Manager with an error exclamation point on it, now it shows up as just "Arduino Leonardo", with no exclamation point.