Leaving aside the semantics question of what's "Technology", what is "Engineering" and what is military doctrine, we can definitely see that the Japanese military had a qualitative edge over the Americans at the outbreak of the war. This advantage dissipated gradually, but was clearly reversed by the fall of 1943.

The IJN main Carrier mobile/strike force, "Kido Butai" was the most powerful naval unit in the world in December 1941. The pilots of the Imperial army and navy were combat veterans of the war in China, flying cutting edge aircraft. In particular, their pilots had aircraft types that worked, and the pilots were practiced in, anti-shipping attacks. Long ranges of Japanese aircraft were particularly suited to the Pacific war.

Similar to their aircraft, Japanese naval forces had modern technology and were well practiced. Their Torpedoes worked. They were trained in night battles and so forth.

The Japanese qualitative edge began to slowly erode over 1942. The first important technological factor was American Radar. This innovation provided warning of incoming Japanese aircraft and offset the training advantage of Japanese surface forces in night fighting. Radar was a gradual innovation over the course of 1942-1943. It mattered a little bit at Coral Sea in May of 1942. Radar became important in the night surface actions off Guadalcanal in the fall of 1942 and was a key factor in the actions which the US Navy got upper hand. By 1943, radar fused shells were introduced which considerably improved anti-aircraft gunfire by surface ships.

In terms of aircraft, 1943 was the year in which new U.S. fighter aircraft appeared in the war. The P-38 rolled out gradually between December 1942 and May 1943. Land based F4Us were deployed gradually in early 1943. The F6F was deployed in August 1943 from carrier decks. These types were clearly ahead of Japanese fighters in overall performance.

American attack aircraft also begin to improve in performance in late 1942 and early 1943. Skip bombing was introduced in late 1942 and gradually replaced ineffective high altitude attacks against shipping. TBF avengers replaced the obsolete Devastator in the summer of 1942. The U.S. ability to successful attack shipping and control the sea-lanes by air was complete.

While the Japanese edge in 1942 was composed of more complex factors than just "Technology", technical innovations were a key part of the story of the Allied reversal of this edge. This reversal took effect gradually over the summer and fall of 1942 and was largely complete by the end of 1943.

the U.S. forces shot down 350 Japanese planes in aerial combat while only losing 30 themselves

Well this was just because the Japanese Zero fundamentally lacked for defensive capabilities. Most air based weapons intended to fight other aircraft wouldn't struggle to puncture the aircraft, Zero's were poorly armored, and the lack of sealed fuel tanks meant they had a habit of bursting into flames.

and superior technology

This is actually something of a misnomer. The Zero wasn't actually a feat of technology- the Japanese could only match the industrial output of Italy and the quality of their manufacturing was largely suspect in some key areas. The US and Soviet Union could weld just about anything, and the US was extremely advanced for the time in terms of cast metal parts. The Japanese made heavy use of rivets and while in some areas this would prove some what antiquated- Japan was still using riveted hull tanks at the end of the war- it was standard for aircraft.

Instead, what made the Zero such a devastating aircraft was owed to the fact that it was stupidly simple. Japan had limited reserves of strategic resources- aluminium and oil- so the aircraft was extraordinarily light. The frame (emphasis on frame, it'll come up later) was extremely durable as an air frame because it was a single piece instead of two that were joined together like many American aircraft of the era. This combined with the use of flush rivets (traditionally rivets had a bulb on the driven side that whatever you were using to drive it would impact and the far side would have something pressed to it that'd mushroom out, forming the fastener, with a flush rivet the rivet hole is instead counter sunk and instead of an exposed bulb the rivet sits inside the frame) and attention to detail- the guns sat flush against the air frame- lead to an extraordinarily maneuverable aircraft that made effective use of the resources available to Japan.

It also meant the thing had problems. It was a competent design in 1940, but it wouldn't take long for flaws to be found, the two biggest being that these aircraft had almost no armor to speak of to protect the pilot, and the fuel tanks had zero protection. The lack of pilot protection lead to something of an experience crunch- even after the Zero was outclassed people who knew what they were doing with them were still a perfectly capable threat- while the lack of hermetically sealed fuel tanks meant that it wouldn't take much to make a Zero burst into flames. The relatively low top speed for the Zero also meant that these aircraft were wildly vulnerable in a dive.

So it's inaccurate to claim that the Japanese had superior technology, but instead were clever engineers. Indeed, the reason the Zero stayed in production as long as it did was owed to the fact that the Japanese lacked the means to really build a superior craft- delays and production issues meant that any replacements wouldn't exactly see the light of day, this being relative to the US who went from the F4F Wildcat- which wasn't exactly old technology (the Zero could out-turn Wildcats like it was no one's business but Wildcats could sustain a dive, which Zero's could not) it just was ill suited to combating the Zero- to the F6F Hellcat and the F4U Corsair in a matter of 2 or 3 years relative to the Zero's introduction. This was something the Japanese fundamentally could not imitate.

The Japanese- much like the Germans- never really eclipsed Allied technology at any stage in the war. They were dramatically more willing to press available technology into service before it may have been ready, with the German ME262 being emblematic of this issue, but they didn't surpass Allied technology or manufacturing capabilities. While the classic example would be the disparity in battleship technologies- the Bismark could accurately lay fire on a target as long as they could see it, the Iowa could lay accurate fire on a target beyond the horizon, in a storm, at night, in the middle of a 350 degree turn just to dab on them- aircraft were not exempt. The Zero made use of a Nakajima Sakae engine that produced about 950 horsepower and was only just coming off assembly lines in 1939. The Boeing B-17, which the Americans didn't even keep in mainline service for the entire war, had four Wright R-1820 Cyclone engines that each produced about 1200 horsepower, and that was an engine design that originated in 1925! All this also ignores the fact that Japan fundamentally couldn't even build four-engine heavy bombers.

Instead the Japanese took what they had available and made effective use of it- while under powered as far as an engine went, Zero's were so light that they could afford to sip fuel, and it gave them a range no American aircraft could match because all that extra performance came with cost.