All countries, especially outside the EU, have differing laws on import/export and taxation.
I have heard of similar situations to yours and would advise that you sell your cars in UK and buy a car/s locally therefore avoiding the tax - if you still can. If you are already stuck with the tax bill for about twice what your cars are worth - unlucky.
It is your personal responsibility to find out details like this BEFORE you take your cars with you whichever country you end up in!
To answer the original question, LOA is to compensate for the additional costs associated with living abroad, not to pay for personal tax bills. This is not an LOA issue it is a personal admin matter.
As for SSLOA - no idea as I don't know where you are, however, you must be administrated from somewhere (as you are already receiving LOA), ask them.