I would go back to them today and advice the following.

That they were being paid to provide a service and whilst providing that service the item was under their care of control.  Furthermore though they are statutory corporation they are not exempted from common law negligence claims.  Therefore if such a claim were made it will fall to them to provide details as to what happen to it, and if what happened to is anything other than an act of God, negligence is proved.  In the alternative, if they can’t prove what happened to it, negligence is also proved.  So the fact you didn’t pay them more to look after it better is irrelevant.

In any even event, the fact that there is a backlog is not your problem. It’s theirs.  You have waited a reasonable amount of time and it’s time to get it sorted out.

Therefore and you want it sorted within 7 days or you will be lodging a complaint with the Postal Industries Ombudsman.

You may also want to remind them that, as they are not exempted from common law negligence claims, statements such as “unless I had insurance they are not legally obliged to provide the value of the items lost to me’ can only be construed to be a statement designed to be both deceptive and misleading, which on its own, would warrant a complaint to the ombudsman.  That is the fact that they are not required to make a discretionary payment in connection with an in-house discretionary claims process doesn’t translated into they are not legally obliged