Basically they can ban you for whatever reason they want and they're not obligated to tell you why. In my experience, however, they've been very reasonable in dealing with account issues. If I were you, I'd simply explain my situation and hope for the best. Write a detailed list of your systems and used software (HKN etc.) along with some links to blue posts. Ask politely if any of the used software you've listed is a violation of the terms. If you've done nothing other than what you've stated, you should be ok :-)

Edit: Assuming of course that all your accounts are in the same name, haven't been shared etc etc