I recently read Last Stand of the Tin Can Sailors and the Japanese attack was depicted as overly complex and byzantine. Assuming that this was not just the case of commanders desperately throwing all remaining forces at the Allies, was there any longer term plan of reversing the tide of the war?
According to Thomas Cutler's The Battle of Leyte Gulf the "logic" (if you can use that word to describe anything Japan was doing by 1944) was that a serious enough defeat off of the Philippines would weaken American political resolve. This in turn would result in the United States agreeing to a negotiated peace settlement on terms that were acceptable to Japan.
Re: longer term plan, Japan never had a realistic plan to knock the United States out of the war militarily. Even at the height of their military success prior to the battles of Coral Sea and Midway they never had the ability to land a "knock out blow." They harbored vague fantasies of eventually invading Hawaii, but for logistical reasons that was little more than a dream.
To get back to 1944, even if Kurita hadn't turned away from Taffy 3 and had wiped out the American CVEs it would not have had a meaningful strategic impact on the war. The human losses for the USN would have been brutal, but losing six escort carriers wasn't going to alter the course of WW2.
While Kurita was finishing Taffy 3 off he would have been under constant attack by aircraft from the other CVE task groups. Additionally, Adm. McCain's TG 38.1 was getting into airstrike range, so if he'd stayed around much longer Kurita would have been hit by the full weight of Halsey's most powerful carrier group. I can't envision any realistic scenario where Kurita does anything more than sinking a few extra DDs and CVEs off of Samar.