By all means go ahead with your IAS appeal. However, it is regarded as an exercise in futility as you are dealing with an incestuous cartel of ex-clampers and their mendacious, roboclaim solicitors and debt collectors who will, in all probability, reject your secondary appeal.
Not to worry though. Any appeal rejection by Excel or the IAS is not binding and does not affect the most likely way you will see off this scam, which is typical of Excel, if/when it goes to court where a truly independent arbiter, a judge, will decide whether you owe Excel a debt.
It would appear that you have the evidence that you paid for the parking but there appears to be a disconnect between RingGo and Excel. In my opinion, there is no need to SAR Excel at this stage. You should only SAR after you receive an actual claim as it is very likely that the particulars of claim will be so woefully inadequate that you can probably see the claim struck out well before any hearing.
I am not a user of RingGo (or any privately run car parks if I can avoid them) app user. However, send a SAR to dpo@ringgo.co.uk to see what information comes back that can be compared to the evidence you have of the payment. You may have to provide non-photographic evidence of identity, which in your case would be a copy of the front of your V5C car registration document.