I've not watched the video yet, but had TF 34 still been in the area... it would not have gone well for the Japanese at all.
Just an examination of the battleships involved paints a striking difference...
On the American side there were four of the most modern, capable, and up-to-date battleships in the world: Washington, Alabama, New Jersey, Iowa
All were armed with 16" rifles firing the exceptional super heavy armor piercing shell. More importantly, all were equipped with the best fire control radar in the world, and all four were well armored against the older Japanese ships.
The Japanese fielded 4 battleships as well, the Yamato, Nagato, Kongo, and Haruna. Yamato was armed with 18.1" guns, Kongo and Haruna with 14" guns, and the Nagato with 16" guns. The Kongo, Haruna, and Nagato were all of WW I-era vintage, and their shells weren't particularly well designed, while the American 16" shells could penetrate the armor all of the Japanese ships (except Yamato) at virtually any range.
During the naval battles around Guadacanal the Kirishima (sister to the Kongo and Haruna) hit the USS South Dakota with at least 3, possibly more, 14" shells, which failed to penetrate the SoDak's armor. During the exchange, USS Washington engaged Kirishima at virtually point blank range and savaged her with multiple main and secondary battery hits.
During the actual battle, Kongo had already been slowed by torpedo damage and was struggling to keep up with the rest of the Japanese force.
My guess as to how it would have played out?
Two older Japanese battleships sunk, one older battleship badly damaged (and later sunk by air power) and the Yamato severely damaged by the combined weight of 36 American 16" rifles.
On the American side, 1 badly damaged ship, and three with light to moderate damage.