Yes as far as I’m aware you can just apply for a new one! That is my plan too, jet back to the UK after three months in Oz from December then apply for a new eVisitor, all depending on PMV situation.
I hear you - all the arranging while you still have to consider visa timeline is driving us nuts. I work in Shanghai but my visa expires there in February, so we have a short window of desireable time to juggle with?