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Unfortunately, a discharge of this sort is intended to be permanent. The passage of time and your post service accomplishments, while certainly a credit to yourself, aren't legally relevant to the issue of a discharge upgrade. This is because the only considerations for the board that does upgrades are whether or not the discharge was incorrectly given or an injustice when it was given.
You can only appeal to the DD Form 149 military records corrections board at this point, and you can only do so if this discharge was granted by a Special Court martial. If you got the BCD from a General Court Martial, the DD Form 149 board can't even review it.
If it was a Special court, then you'd have to prove that the BCD was given in error (meaning it wasn't actually legally available for the offense) or that it was an injustice at the time you received it. The injustice argument is where most people apply, by showing that evidence wasn't considered or that there was an unfair bias applied to their case.
If it was a General discharge, you have no method now available to appeal the discharge or upgrade it. You could move for a pardon of the conviction from the President, through the Department of Justice, but that would only remove the federal conviction. The discharge status would still stand.
As for advancing, while there is no absolutely prohibition against hiring those with a court martial conviction, it's not practical to expect either to be hired or advanced in the government with a conviction.
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