Given my limited knowledge of this subject, it seems the US Navy was quite successful in hurting the transport of oil from the Southern Resources Zone back to Japan. Did the Japanese consider moving their Navy southwards to mitigate this problem?
For most of the Pacific War, the Japanese Navy had a major presence at Truk (or Chuuk as it's known now). Truk is (very) roughly about 1000 miles north of Australia, and a similar amount east of the Philippines. Essentially, the bases at Truk were Japan's version of Pearl Harbor.
It wasn't until Feb 1944's "Operation Hailstone" smashed the base that Japan stopped using it for its Navy. Even then, however, it remained a formidable military base; it was isolated and left to wither by an island-hopping US military strategy.
The problem wasn't where the IJN was located, but what ships the IJN consisted of. It wasn't until quite late in the war that escort ships designed to hunt submarines started to come into service, and they weren't particularly good. Destroyers in the IJN were traditionally used to whittle down the opposing battleline with heavy torpedo salvos, not kill subs.
Anti-Submarine Warfare was Japan's Achillies' Heel.
The IJN did move to bases in the Southern Resource Area, in order to protect it, and as bases for further strikes elsewhere. The IJN's major bases in the SRA included Singapore, Rabaul, Manila, Cam Ranh Bay, Staring Bay on Sulawesi, and Lingga Roads in the Malacca Strait. They also operated from Babeldoab and Palau in the Carolines and Truk Atoll. Truk and Singapore were probably the two most significant of these bases, with Lingga Roads coming a close third - Truk protected the eastern end of the SRA, while Singapore fulfilled a similar role in the west. Lingga Roads was used as a staging area - ships based at Singapore would commonly cycle in and out of the Roads. All of these bases allowed them to maintain an effective surface control of the waters of the SRA until the Allies committed a vastly superior force.
However, the main threat to Japanese merchant shipping between the SRA and Japan didn't come from surface ships or aircraft. Allied submarines were the only threat capable of threatening the shipping lanes of the SRA for much of the war. The IJN had a very poor anti-submarine doctrine, partly due to an institutional focus on the offensive. This was compounded by limited experience, and a lack of effective ASW weapons and sensors - they never fitted SONAR to their ships, nor an ahead-throwing weapon like the British Hedgehog or Squid, which proved to be the most effective surface ASW weapon of the war. This meant that Allied submarines could be hugely effective, despite the early failures of the American Mark 14 torpedo.