What if the Japanese won the Battle of Kokoda Trail?

OK the Japanese win the battle(s) and get over the Owen Stanley Mountains. Exactly how many Japanese are now ready to march on Port Moresby? How much ammunition do their have or food. All supplies for this march and attack have to come over the trail, so their logistics suck. The Allies can reinforce Port Moresby without interference, and the Japanese forces approaching Port Moresby will be under air attack with no defense, and the waters between Australia and New Guinea are controlled by the Allied Navies and airpower. Even if the Japanese do take Port Moresby the Allies will have the opportunity to wreck facilities - and any repairs will have to be performed with hand tools. Until the Japanese can land supplies by sea the troops in Port Moresby will be on their own. Even if the Japanese can fly in some aircraft after repairing the fields, how do they resupply with gasoline, ammunition, and bombs to contest Allied air forces. The answer is they can't, even if the Japanese use every transport aircraft they own they can't sustain an aviation element in Port Moresby. In fact, between the track and air supply they will be lucky to provide enough food and ammunition to sustain the garrison.

If the IJN wins Coral Sea and the IJA takes Port Moresby then it becomes a viable outpost - but no more. Annoying raids to N. Australia, but once the Allies build up air power in N. Australia and close the sea lanes it simply becomes a place where the Jpanese slowly starve.

while meanwhile the Battle of Guadalcanal begins in August with its serious strain on Japanese resources as King and Nimitz have their own resources that are unaffected by events in New Guinea
 
I really don't see the Japanese taking Moresby overland. Sure , they could give the Aussies a bloodier nose in the jungle than OTL, but once they hit the area around Moresby itself... Well, look at it this way, August-September 1942:

The Japanese have whatever is left of 6000ish men and between 8 and 13 (depending on attrition) mountain guns at the far end of a track that makes resupply effectively impossible.

The allies have two CMF infantry brigades, two (or three if late enough in September) AIF infantry brigades and various odds and ends (elements of two local militia battalions, various rear area troops, engineers, stray RAAF ground staff etc.) minus whatever is lost on the Kokoda Track itself (order of 600 men IOTL, possibly 1200-1800 in a realistic worst case) with two US infantry regiments (roughly equivalent to in strength to a British Commonwealth Brigade) arriving in September; at least two field artillery regiments (24 guns each) plus a scratch battery of mountain guns; two 6in and several 6 pounder coastal guns (with an additional possibly four 155mm guns depending on the date) and up to three heavy and three light AA batteries (12 guns per heavy battery). And if they can hold the harbor, they're able to be resupplied rather easily.

Now, as always, there is the possibility of things going catastrophically wrong for the allies. But with that discrepancy in firepower (8-13 75mm mountain guns vs 48 field guns -admixture of 25 pounder, 18 pounder and 4.5in-, 36 heavy AA guns, 36ish light AA guns) and logistics, I know who I'd bet on.

*If* you want the Japanese to get Moresby I'd suggest Coral Sea going the other way is the best set.
 
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