https://kindlemodding.org/jailbreaking/WinterBreak/ says it's based on https://kindlemodding.org/mesquito/ which in turn says it needs <=5.15.1.1

That's a mistake on my part, I've updated that page

Right now WinterBreak remains unpatched, but it is patchable and likely will be in the near-future

Is there a better way to block OTA updates than renametoabin? I've tried that and a few alternatives and none help with my Kindle 4s disabling the jailbreak whenever they get a whiff of internet.

Yes, but you can disable OTA updates