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