Only one of the online processors accepts state estimated tax payments.

I live in California, and unfortunately the California Franchise Tax Board (FTB) is an IT disaster. A few years ago, in the glory days of AmEx giftcards, I did make three separate California estimated tax payment in a particular quarter via Official Payments. I received the email confirmations of the payments from Official Payments. However, the FTB failed to properly credit my payments and this later caused a major hassle. (This is only one of several major errors the California FTB has made over the years.)

So yes, I do think you can split state estimated payments. But I no longer do it because I'm too afraid of another major SNAFU from the FTB. If you try it, hopefully New York is smarter than California.