I can see where you've already made the conversions I was thinking about when I suddenly realized where you were located...I thought the "120v isn't available" should have jumped up and hit me in the face!
I think from a cost effective standpoint, as you've already discovered a 220v refrigerator is going to be costly, my choice, were I doing it, would be the step-down transformer inserted between the converter and the refrigerator and if you are camping in the bush for longer than the 8 days you get from your current LP setup, a spare tank or two of LP would be easy enough to procure and transport. At least, in the above changes, should you have an "issue" with a component out in the bush, repair parts might be easier to come by. I would carry an extra "US Specification" controller board, though, to handle failure of the controller. Dino makes the better boards and they should be relatively cost effective even with transport down under. You may even find a local supplier that stocks the boards, as, while it may sound rare, I understand that it isn't all that unusual for Aussies to import US made caravans. I am surprised though, that the 3 way refrigerator is still common in your environment. Up here, they've, for the most part, gone the way of the dinosaur, even in the smaller applications, they are starting to fade away. It may be that here, the preponderance of generator usage and full hook up CGs has more or less spelled their demise.
Lithium batteries have so many advantages over lead acid, that I think, in the near future, most rigs purposely modded for or designed for "boondocking" up here and "bush camping" down under, will be using them. The biggest hinderance right now is the charging changes and the question, up here anyway, of the chicken and the egg. Will the converter manufacturers start making converters with Li specific charging capacity or will they wait and give up the change to third party vendors as more folks make the change and Li batteries come down in price. Or will folks make the Li change and cobble together their own charging systems and thus negate the converter manufacturer's need to make any design changes until forced to...
Sounds like you are "on top" of everything, good luck and happy camping!