Good for you. I'm sure, between you and the legal system, you will prevail. I would expect a judge to grant you a CCDW license and thank you for your honesty. You don't seem to me, from what I have read here, to have a propensity for violence towards yourself or others. That is what this comes down to.
Any advice from the Lawyers 64? If it's not too personal it would be helpful to this great website. You are not alone, all the best to you in your appeal.