If a
Kawanishi N1K carrier variant was tested, perhaps their
J6K would have been in the cards.
The J6K Jinpu was not carrier based; it was a land based naval fighter and reached mock-up stage only before the war's end; even then the mock-up was based on the J3K1, which only existed as a mock-up. It was Kawanishi Type 17-Shi Land Base Fighter, while the J6K was Kawanishi 18-Shi Land Base Fighter, named Jinpu. The former was cancelled at the beginning of 1943 because they couldn't get the supercharger to work. The Jinpu was cancelled in July 1944; it was to have derivatives of the same engine as the A7M Reppu, the Nakajima MK9 Homare, but supercharged.
The N1K-3 and N1K-4 Shiden-Kais that went down aboard the Shinano were carrier fighters modified with only a tail hook, but no wing folds - they were only intended as interims until the A7M Reppu and derivatives was ready, which was what the IJN was hinging its carrier fighter future on; that and continuing development of the A6M.
As for the Reppu, yes, delays dogged the project, largely because of IJN interference in the choice of engine and technical details, also it wanted Mitsubishi to concentrate resources on the A6M and G4M and addressing J2M Raiden issues, which all stifled its development. The big earthquake on 7 December 1944 damaged the factory where it was being developed, destroying drawings and manufacturing jigs, which effectively ended production before it had really begun. The promising and good looking Ki-83 heavy fighter production and development was also affected by the quake. A design derivative of the A7M3, the Type 20-Shi Carrier Fighter was proposed, to be jointly developed by Mitsubishi and Nakajima but nothing came of it before the end of the war (The internet has designated this the A8M Toppu, but that is a red herring - the 20-Shi fighter was based on the A7M3).
If the war had continued, the A7M would have been opposed by the F4U-4, P-47N, P-51H, F7F, F8F and the P-80 , all of which rendered the A7M obsolete from the start.
The IJN was incredibly short sighted with regards to manufacture and design of new aircraft to meet the US threat. Its entire strategy appears to have been knee-jerk, producing designs to meet threats as they emerged, rather than examining potential future threats and planning long term. There was the lure of jet power, notably the Nakajima Kikka, which first flew on 7 August 1945, the day after the Hiroshima bomb was dropped, although the Kikka was ostensibly land based (although its wings outboard of the engine nacelles could fold, there was no hook or specialised gear for carrier use).
It was designed purely as a fighter powered by the new powerplant, from which information came from the Germans, rather than a long term strategy to develop a next generation fighter, despite interim work that had been done in japan on gas turbine engines. It's principal role was as a land based interceptor for countering B-29s; later versions were going to be fitted with heavy cannon. Production of a jet based on the Me 262 was considered in Japan, the Nakajima Ki-201 for the army, but no work was done in terms of hardware.