As a modern experiment, your approach is excellent. However, concerning historical Mayan, Vedic, Greek, Egyptian, Babylonian and Chinese mathematical astronomy methods must be tested against nearby cultural astronomical methods,
1. Needham has shown that the Chinese Remainder Theorem arrived in time fore Diophantus, 100 AD, to write several books on indeterminate equations. At this point Pythagorean "great year" data recorded in quotient and remainder math has not been linked to the CRT. The Silk Road likely opened well before 100 AD. Had the CRT and generalized indeterminate equation solutions to astronomical and every day problems arrived earlier, a major window to ancient math would be opened.
2. R.C. Gupta reports Vedic CRT data in ways that may link to China and/or the Mayan world. The Chinese and Greek arithmetic was quotient and remainder based. The Mayan arithmetic only used quotients. Hence, Vedic astronomical records can easily be classified as Chinese or Mayan by inspecting the writing out of quotients and remainder (Chinese) and quotients only (Mayan).
3. The largest Mayan "great year" should offer a hot debate. Discussing possible, likely and confirmed LCMs and GCDs of Mayan 260, 360, 365 1/4, Mars, Venus, lunar and other planetary objects requires scholarly considerations that go well beyond this summary.
Thanks again for discussing this topic in great depth, and simple modular arithmetic used by Chinese, Vedic and Mayan mathematical astronomers.