This would have been difficult to manage. First, the Japanese were running on empty and needed to retire and refuel, particularly their destroyers. Second, the US really did not have a firm fix on where the Japanese fleet was, its composition or, its course. All of this would have been necessary for even attempting a sorte against it.
Also, the US Navy was not about to send just a surface action group (to use the current venacular) out looking to engage the Japanese on its own. Without air cover(ie., a carrier or carriers) such a group was highly vulnerable to air attack....something that was pretty obviously the Japanese strong suit at the moment.
Lastly, even if an attempt was made the distance between the fleets was sufficently great that interception was not likely.
No, the best thing for the US to have done was what they did originally; hunker down in a defense mode, lick their wounds and, live to fight another day.
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