After escalating to a supervisor, I did get a rational response from CLARC. As I heard it, CASA considers that CAR5 licences are no longer legal licenses, which is why they will not confirm them.
Don't ask why we can still fly on CAR5 licenses, I just didn't want to go there.
CASA has undertaken to issue me a new Part 61 license within 1 week. You heard right - 5 business days!!!
So, now I have a fistful of logbook pages and photos to be certified so its all in Canberra ready for Tuesday and we'll see what happens.