So while I follow your reasoning I still believe that Australian forces will be concentrated in Malaya.
The main reason for this is that Australia want's the AEF as one cohesive formation. The splitting up of Australian divisions by the British was a point of contention after all. After fighting is over in North Africa represents an ideal time for this to happen as their won't be any other active land theatres. The only question then becomes where do the troops go to get familiar with each other and work out kinks in the command structure etc.
The Middle east makes a good bit of sense as their is plenty of space to train and most of the troops are already there. There is still the issue of Japan though. Australia will be very wary of Japan and will want it's troops back east to face off against the Japanese threat.
So the next choice is bring them back to Australia, still plenty of space but most of the units are a long way off and in Australia they are much less of a deterrent to Japan.
The only other possible option is Malaya, it directly faces Japanese territory so is a good deterrent and has a good amount of space to train up troops. The other advantage is that is is a good half way house between Australia and the Mediterranean. That for me is key as this is not meant as a combat posting, more a training and deterrence posting. Once the Japanese back down or a deemed not a threat then the Australians will be sent back to the Mediterranean(once they are trained up). The training aspect is key here for me as the 8th Australian and 1st Australian Armoured are still working up. Add a British Armoured Division to both help build up the Australian Armoured and give the 8th a formation to train with that is ready to go and you have a decent force.
Again though this is meant as a training deployment more than anything. Their will be several months to a year at least before Britain is going to be conducting any major amphibious operations anywhere in Europe. You can afford to sit the Australians in Malaya for that time while they work up and then bring them back when everyone is ready. After all the Japanese won't do anything with a 4 Infantry and 2 Armoured divisions in Malaya will they.
As for Britain needing to be seen as doing something. Firstly the RAF will be in Malaya in greater strength than OTL as will the Royal Navy. The Navy is a far bigger deterrent than a British Division so will be appreciated. Plus their will likely be a division in Malaya to help the Australians get up to speed and other formations spread around. Reinforced Brigades on Rabul, Ambon and Timor wouldn't be unappreciated I'm sure.
The next major offence the British are likely planning will be Rhodes. You don't need the Australians for that, British and Greek troops will be plenty. Then after that it will either be Sicily or Norway in some form. If it is Norway are Australians the best choice?. Even if it is Sicily it will be mid 42 at the very earliest before Britain will think they can be ready.
The politics are simple. Australia want's its forces concentrated and this is an opportunity for that to happen. Britain can't object too much as what else is happening. Plus for Britain the Navy is the main line of defence and they can send some troops anyway as they have some to spare.
First, can you stop referring to the “AEF”? It was the 2nd Australian Imperial Force.
Second, Australia did not historically demand that its entire forces in the Middle East be redeployed to the Pacific until after Japan entered the war and had such early successes.
Third, Australia had a division earmarked to defend against Japan, so it’s not like they were averse to having some divide in their forces.
Forth, Malaya and Singapore are the responsibility of the British. The idea of sending the entire 2nd AIF there seems way over the top. Until the Japanese enter the war, which was not certain until it happened, they’d be on garrison duty. Australia declared war on Nazi Germany - and later Italy - and wanted to fight. They’re not just going to pull all forces back home, effectively, to face the Japanese threat because the Empire has the upper hand in North Africa.
More realistically, I could see one division being withdrawn first to Australia and then shipped to Darwin to provide brigade-size garrisons, allowing all of 8th Division to be concentrated in Singapore. The other two Australian divisions would remain in the Med, and may be joined by the 1st Australian Armoured Division, which the British should, in this timeline, be able to equip.