You connected from the same IP as all 13 reconnect attempts. They may all be different acounts, but since we cannot confirm or deny you are a different player, the account will stay banned. The best route would be to have the person originally banned make an appeal.
Reading throughout this app I can see that you are genuine in your apologies. I personally don't think that you would hack again if granted the ability to join the server. Although what I'm struggling with is the amount of evasions that were attempted before creating this appeal. I think you should be given a duration ban of the staffs choosing due to the amount of evasions as this is an entirely different situation than just hacking. Actions have consequences and ban evading is one of them. -1