Great story. I love your details. Too bad that Linear A and its math have not been decoded in sufficient detail to report calendar calculations. Only a a few Egyptian binary fractions ... that look like trading units ... have been published by Struick.
Calendars offer wonderful windows to the past. Like the multiple Mayan calendars, the exact arithmetic that reported 405-lunar cycles, the everyday math of the Mayans is unknown. I like Floyd Lounsbury's approach.
Stressing calendars from a particular culture offers wonderful news, in my eye, if and only if, the scholar is humble about the related numeration foundations that actually built the ancient calendar(s).