Not looking for support yet. but just wanted to chime in that I have the same issue with one of my sites on Siteground.
All plugins and themes are disabled. Sometimes the backend dash works and sometimes it does not. The only fix I have is rolling back Core to 4.4.x but I must roll the database AND the files or I still have the memory issues.
I am still investigating and will report back if I find any clues.
