For both of you please understand a few things. One, we are unable to ban your accounts. This is a community forum. There is no legitimate appeal system for bans. Second, I personally have created this OP, or thread, to draw attention to cases just like yours of genuine and honest players who are being caught in a faceless and unfair automated ban system. I truly understand and feel your despair and anxiety.
I have only had one of my accounts banned before and it was a deliberate attempt by me to do so to draw attention to the failure of the system and loss of Bungie's interest in ranked play. Because of the sheer positive statistics of that account, my posts in their forum while they managed the game and what I was able to accomplish before the ban got me an invite to play and audience with an actual Bungie employee. Though there was no resolution to my concerns at that time, I respected the personal contact that I finally achieved.
This thread will stay pinned in any hopes to draw further attention to your concerns. Thank you for allowing me to use your stories to gain notice to this issue.