In reply to Sean.

I'm experiencing the same thing Sean. I'm also with Siteground (1.5 years) and for the first time in 11 years using WordPress I'm seeing core.xxxx files. They're populating every few minutes. Mine are bigger than yours (starting at 150MB and quickly ramping up to 350MB until the server stops them from being created.

I'm crossing my fingers it's something that will stop happening in a new release. Until then, I've disabled as many things as I can, and delete the files throughout the day.