I would not say these Japanese Navy tactics are "Advanced". They were the same hit and run dogma everyone bought into during the early monoplane era of the 1930s (despite requiring, in practice, an unaware target and point-blank fire to make the guns effective at overtaking speeds: Turns in reality easily broke diving attacks); a dogma which took most of the War to moderate to its proper place in the Luftwaffe's case (or never, in the Japanese Navy's case).
To their credit, the USAAF in Europe was among the most intense users of prolonged low speed circle fighting (over multiple consecutive circles), which avoided attacks and trapped targets for a prolonged period at a constant range. This all you you'll you hear the P-47s do (especially the Razorback, despite the mushy initial turn of all P-47s), and similarly all you hear from P-51 pilots is the constant use of flaps in turns. They would even ask about each other's flap settings over the radio during turning combat!
I vaguely recall that the Japanese Navy used the vic throughout the War, and that this was contrasted to the Army using the finger four at some point.
As to the Sakai dispute, having suffered head wounds in combat does not make you immune to criticism.
My understanding is that air-combat tactics began with turn-fighting and then evolved into squadron-based, coordinated attacks. There are numerous references to energy tactics going back to World War 1.
Oswald Boelcke's rules for combat were basically to:
1. Attack out of the sun.
2. Attack in pairs.
3. Get altitude advantage.
4.
Do not run from the enemy.
These rules promoted turn fighting rather than energy tactics or mutual cover tactics. Energy tactics and beam tactics evolved in the pre-war period and early war period.
Energy tactics oftentimes relied on maintaining energy through attacking and then climbing.
This post on Reddit describes both the section tactics and the individual looping tactics used in section fighting by the Japanese Naval pilots, as described in "Sunburst". My understanding is that everyone was using energy tactics.
The defensive "lufberry" circle was used by slower aircraft, with greener pilots, against fast aircraft which were employing dive-and-zoom tactics (energy tactics). The Japanese heavily favored Lufberry tactics because their pilots had less training and they were oftentimes flying slower aircraft.
The 343rd AG used beam tactics, according to Genda's Blade, which seemed to have been necessitated by the adoption of four-plane Shotai, instead of the three-plane Shotai. The four-finger formation supposedly was designed for mutual cover (beam tactics). I also remember reading that there was supposed to be a shooter, with the second plane providing cover. Getting back to the main subject, Shoichi Sugita was known for relentlessly drilling four-finger and beam tactics into his students.
The Japanese in general moved from three-plane formations to four in 1943
1944 and 1945. According to several sources, but mostly Sakaida, the third man in a formation would normally not return from missions. I've read, but can't remember where, that US pilots typically focused attacks on the third man because he wouldn't have any cover.
Japanese pilots, such as Sadaaki Akamatsu would claim that they had the best maneuvering (or dogfighting) tactics in the world. But I think he was speaking more about how veteran Japanese fliers had training in how to best leverage aircraft which had great turning abilities.
EDIT: The IJN and IJA switched to finger-four tactical units in 1943, according to Shores, Hata, and Izawa's books. It's interesting to note though that vics continue to appear in reports from Allied pilots well past 1943.