Do you know 2 console ID's attached to your account? Appeal an investigation on your account and try until it is escalated to the enforcement department. Try convince them your account had UA while you have been "Absent", by absent I mean when the account was on Console ID 1, the investigation team will see the absence of time between console ID 1 and Console ID 2, they should regard the Console ID 2 is the "hacker" and this is evident for your appeal.
I got my account all the way to the end of the report, however I could not establish Console ID 1 (xbox.com does not allow you to view it once you are banned). So they had to note the escalation left for the representative was "Console ID was not confirmed, so no evidence of unauthorized access).
This is one technique I know of. I don't care if people flame and say this won't work, I am trying to source a solution. It's a logical process of support escalation and if you have the evidence and story to back it up you should be fine.
Closing this thread, other members will say that you can not.