According to the uploaded 'reminder' letter, the amount of the penalty fare due is said to be £100, and no payment has been made. Since the correct amount of a penalty fare is £100 PLUS the full single fare for the journey authorised by the penalty fare, I do not see how a valid penalty fare could have been issued for £100 only. Of itself that suggests that there is some error in the operator's record of the penalty fare said to have been issued, in turn adding credibility to the OP's account that no penalty fare was ever charged.
The alternative argument is that, even if the appeal panel does not accept the OP's account that no penalty fare notice was ever issued, the fare of £100 charged could not have been the correct amount for a valid penalty fare because it does not include the “full undiscounted fare” element. That must mean that any penalty fare charged could not have been not charged in accordance with the requirements of the penalty fares regulations. This is the ground of appeal set out in Regulation 16(3)(a). If the second appeal panel accepts that the wrong penalty fare was charged Regulation 17(4) requires that panel to uphold the appeal.
I believe full documentation of the penalty fare under appeal should be available to the OP on the Appeals Service website and consequently it should be possible for details to be downloaded from AS of what form the penalty fare notice is said to take. I assume such will details include particulars of the journey the notice is said to have authorised. I recommend the OP to try to obtain those details and re-post them here (omitting personal details appropriately), as I think they may clarify the basis on which £100 is alleged to be the correct penalty fare.
Since, notwithstanding its late receipt, the appeal panel appears to have accepted the first stage appeal as one to be adjudicated on its merits notwithstanding that it was lodged out of time, and has “decided the outcome of the appeal under regulation 16” (Regulation 11(3)(a)), the OP should now be immune from prosecution for an offence under Byelaw 18 or Section 5(3) Regulation of Railways Act 1889. That may also have a bearing on the course the OP is now advised to take.
Edited to add that I've just seen the OP's update - good news indeed!