It says I have 3 device installations, but it's really 3 logins on this same device. Anyone have any idea why it made me 'register' the device each time, and does anyone know a way to fix that?

Was this a reinstallation of the UD device? If so when you install there's usually an option there for existing user or something similar. (I can't remember the exact wording off-hand.) Is that what you're referrring to DT?