Maybe I’m wrong, but I have seen articles that claim that the ash from the eruption 640,000 years ago were 300 feet thick as far away as what is now Illinois. Also, that cities “close” to the eruption, some 300 miles, would be obliterated by the blast, then buried. Their contention that the “unlikely” (repeated as a mantra throughout the article) eruption would deposit ash only 3 feet thick close to the eruption site seems at odds with what I have read before (putting it politely). After all, 1000 cubic miles of ash is a LOT (10 miles per side cube).
Like you, I've also read that the cover would be much thicker much farther out.
If someone is really worried about this, they should try and get a job very close to Yellowstone.
If it is as bad as some scientists claim, then it would be better to be obliterated in the initial explosion than try to eke out an existence on an earth doomed to years of massive crop failures, starvation, and dropping temperatures.