Yes, exiting an airline ’ cyclic’ program back onto the street is a PITA. It is almost as if CASA colluded with the airlines to make it difficult. Like the bad old days with second class endorsement & ATPL second class. Not worth a c full of cold water anywhere else.
As irrelevant as it may be, hiring a Baron for a couple of hours could be the best way to get the right entry onto your Oz licence.
Ask the FAA. Maybe they would accept your C&T record for the last 12 months, but I expect you would still need to be current according to that system. If you were overdue a cyclic you’d probably be screwed.