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Note: Summary of sources below.
Raymond S. Locke is poorly attested in contemporary sources, but he was clearly the principal of Barrington High School at some point in the 1950s, which would likely place him right before Albert Genetti.[1] He is also described as the principal of a high school on Lincoln Avenue in the above source, and I can't find any description of principals that come chronologically before Locke. There may have been a principal before or after Locke -- however, this is unlikely, given the considerable tenure of his immediate successors. Somewhat confusingly, he has a son of the same name who was an exceptional athlete at Barrington High School.
Albert Genetti has a detailed obituary which gives an exact length of tenure (1963 to 1980). [2].
A local newspaper describes Gray as having retired in 2009, which gives him a tenure of 1980-2009.[3]
Naturally, Joseph Hurley follows Gray.