The adjudicator must apply the law and IMO the only options are:
To allow your appeal under one of the grounds which an adjudicator may consider;
To reject your appeal;
To reject but make a recommendation to the authority.
As regards the third option, I am not aware of any recommendation which includes paying the congestion charge only,so I think you're in for the penalty or the discount*.
An adjudicator may not consider mitigation/discretion because these powers are reserved to the authority alone.
In effect, it's now as if on receipt of a PCN you are appealing directly to the adjudicator therefore, as per Incandescent, it's the full chebang. IMO, the style and content of the reps which weren't received are a guide to you only. You should treat this as de novo i.e. as if for the first time.
So, what were the circumstances of incurring the penalty and why was the charge not paid within the allowed time etc.