Shorty:
Let me give you a piece of advice in how to approach this thing. I would not argue that they did not have jurisdiction, that you are innocent, or anything along those lines if you really want the pardon.
The key to the pardon is to take responsibility for your actions, to be remorseful, to explain that the conviction is a stain on your character, and that you've led an exemplary life since the incident and your discharge from the military. In short, you need to show that you've been "reformed." Things like statements from employers about what a good employee you are, from your pastor at your church, about how you always take time out of your day to feed the homeless and nurse the sick, and how you are a wonderful guy who volunteers his time to coach wheelchair bound children to play basketball are examples of things that help the process. These statements should all be notarized. A statement from you about how you were young, irresponsible, and didn't understand the impact or seriousness of your actions at the time would be helpful -- if you also include how you have learned from the incident, realize now that it was serious and was wrong, and worked to improve and rebuild your life following the aftermath of the incident.
If you submit 30 pages about how the military did not have jurisdiction over you or the offense, about how you've been wrongfully convicted, and the like, I would fully expect them to deny your application.
