The above appeal is all you need. As it is likely to be rejected, you will be able to appeal to POPLA once your receive the rejection.
However, have you tried Plan A? You should make a complaint to PALS at the hospital.
Just do as you understand why you should not identify the driver, their Notice to Keeper (NtK) is not replying on PoFA 2012 to be able to transfer liability from the unknown driver to the known Keeper. As there is non legal obligation on the known Keeper to identify the unknown driver, they cannot pursue the known Keeper unless their NtK is fully compliant with ALL the requirements of PoFA.
So, when appealing, as the Keeper only, you only refer to the drover in the third person. No "I did this or that". only "the driver did this or that". Don't tell 'em your name Pike!