The parameters of this what-if are very interesting.
Okay, for my two-cents worth: I'd say the Japanese Navy's advantage of longer ranged guns is only on paper. The US has superior gunnery radar which would allow its cruisers to fire at optimum range accurately and faster before the Japanese battleships can bracket the US ships. This evens out the fight.
As for the air side, I say it would depend on when the naval battle takes place. If it's at night, neither side enjoys air superiority and the US radar advantage would give the Japanese a heavy pounding, thus defeating the Japanese attempt at reinforcement.
If at daylight, the US would have air superiority because the P-38 has better range, guns and armor than the Japanese opposition. Once the US claims air superiority, it would be a simple matter for the US to bomb the Japanese convoy.
The victory would go to the side who can maintain a naval presence in the battle area and keeping the line of supply open to their forces on the island.