Even a decisive-battle victory could leave Japan strategically trapped

Would winning Kantai Kessen have allowed Japan to control most of the Pacific?

No; the battle could cripple both Japan and the United States, leaving another fleet, especially Britain's, able to determine what happened next.

Victory in Kantai Kessen would not by itself have given Japan control of most of the Pacific. A climactic engagement was likely to cripple the Japanese fleet even if it also shattered the Americans. Japan's difficulty replacing ships meant that the nominal winner could emerge unable to exploit its success. In that condition, a British fleet entering the Pacific might be larger than either exhausted combatant. Winning a battle and retaining enough force to turn victory into command of the sea were separate problems.