The most significant assumption effecting outcome of the encounter is the visibility. Also, if the encounter occurs near dawn and in good visibility, then the direction of encounter matters a a lot. If Japanese squadron is to the east, and US squadron to the west, then the US squadron would be illuminated by the rising sun and give the Japanese optical fire control excellent conditions for accurate ranging and aiming. Conversely if the US squadron is to the east and the Japanese squadron is to the west, the US Squadron would be lost in the glare of the rising sun, and Japanese optical fire control would be severely degraded.
The sea state also matter. Yamato class ships are exceptionally good seaboats even for their size, and very stable with shallow and long rolls even in heavy weather. US battleships of WWII era were all mediocre sea boats for their sizes, rolling more severely in heavy seas even for their sizes. So heavy sea will favor the Japanese battleships over American battleships, although it would hamper the gunnery of Japanese CA's even more than the American battleships. Also, very severe sea states would limit the ability of Japanese CA to keep up with the battleships. This would have tactical implications on overall maneuver the Japanese side can make.
Well, we know what the conditions were that morning off of Samar.
The Japanese were in fact coming from the North and at 06:30 were about to bear down on the Taffy 3 carriers, and would soon be turning to the West. It is here that I would place the engagement, the American Task Force coming from the West to engage the Japanese with the Island of Samar behind them. The American carriers and destroyer escorts still some distance to the south. In fact it would be another 18 minutes before the Japanese opened fire on the American carrier group at 06:48. So I would have the surface engagement with the American battleships occurring at about 06:30.
We know that there were numerous showers in the area that morning, in fact throughout the morning and on several occasions in the actual time line the American carriers and destroyers sought to try and make use of (particularly the carriers) these showers to mask themselves from the faster moving Japanese surface combatants. So in our conceptual time line, these showers would also be present and would have to be factored in, along with a significant amount of broken cloud cover, which would also mitigate a significant amount of glare.
Also factor in the piecemeal attacks of the aircraft from at least 3-5 escort carriers in support of the four American battleships, and just as spirited an attack by the destroyers and destroyer escorts of the Taffy 3 group as what actually occurred.
I expect the American battleships would charge directly in towards the Japanese formation, and try tom bring maximum firepower of their big guns to bear in an attempt to break up the Japanese formation as it bore down on the American carrier group, and particularly the American anchorage that lay just beyond it.
In this case however, the Yamato would also have the Musashi with her. If the Japanese Admiral Kurita kept his battle sense about him and did not order an attack at will, in essence, an every ship "attack for itself" in an uncoordinated fashion (as he did that morning against Taffy 3), but instead used his battleships effectively to focus the two of them on each US battleship in turn while he used the heavy cruisers to distract the other battleships and/or provide a buffer against the American destroyers, he might be able to either mission kill or severely damage a couple of American battleships and give himself a fighting chance to win the engagement.
On the other hand, if the American aircraft could do some damage, and if the American battleships could, in turn, focus their very significant combined firepower on first one and then the other Japanese battleships, then they could do the same.
My own expectation would be, given what actually happened against U.S. Admiral Sprague's Taffy 3 alone, if in addition to the spirited and effective attack the Central force faced with Taffy 3, Kurita now also faced TF 59.7, I believe the Japanese Admiral may have turned away even sooner. I do not know this...but given the fact that he actually did turn away when facing Taffy 3 alone, it seems a good bet.
Anyhow, two Yamato class BBs against those four US BBs if they were both handled properly, would have been an interesting contest, with a potential for some horrendous firepower and damage on both sides.