I am obviously not disputing your experience, but wanted to mention that this was not the standard pattern. The standard pattern for forced conversion at L6 (Staff) was either 6 or 7 reports (I don't remember exactly).
> Principal EM
I don't want to be overly pedantic, but there's no Principal EM on Google eng ladders and so it's not entirely clear which level you're referring to.
The IC ladder runs Staff SWE (L6) - Senior Staff SWE (L7) - Principal SWE (L8) - Distinguished SWE (L9)
The Eng Manager ladder runs EM II (L6) - EM III (L7) - Director (L8) - Senior Director (L9)
P.S. I hope I got the EM II/III designations right. I think EM I is L5, though almost never seen in practice.
P.P.S. Confusingly, the IC ladder allows a limited number of reports (the limit increases with level).