So, I haven't heard back from them in 5 days (I replied on Sunday evening). Does this mean it has gone to arbitration? Do I just need to wait it out
You seem to be under the impression that there is some semblance of honesty and independence with the IAS. Just wait for a response. Don't hold your breach and if it is unsuccessful (highly likely), the decision is not binding on you and you DO NOT pay. You just move on to the next phase.
Just a note to say thank you so much! Received the response today, and the adjudicator has accepted the appeal

"I am allowing the appeal on one ground only, namely that the Appellant's vehicle left within the consideration period outlined by the operator. The operator states that the consideration period is 10 minutes for motorists to read the signs and leave. 10 minutes and some seconds is still 10 minutes.
Having considered all the relevant issues raised and the evidence submitted, I am not satisfied that the operator has established that the Parking Charge was properly issued and therefore this appeal is allowed. "