Don't waste two seconds on a phone call. This is a simple chargeback which can almost certainly be made online and because the basis of the chargeback is that the service was not received, does not require you to seek a refund from the merchant vendor first.
Turn your lengthy post into 2-3 short declarative sentences, omit the emotion, and conjecture, and you will be done. E.g.
1. This item is for a toll transponder which apparently triggered a charge at 8:30 PM on [Date].
2. I did not pick up the vehicle attached to this transponder until 10:30 PM. I have attached a copy of the facesheet of the rental agreement to demonstrate the pickup time.
3. This charge does not relate to me and the service was clearly not received by me.
This should take you somewhere in the 60-90 second timeframe and, because the merchant vendor is not Avis, won't affect your standing with Avis.