"Most writings of the Maya went up in flames. We have to reconstruct their methods and fill the gaps from the numbers themselves, and from the astronomical cycles. In other words: we need an experimental approach also in the history of mathematics. We can't just project our modern methods backward in time. We have to allow the ancient ones to have done things their way, and try to reconstruct their methods by way of experiment."
is correct; however, your view omits the actual numeration system and every day math that Mayans used ... that Bishop de Landa and his Conquistadores disliked so much ... experiments are not needed. Code breaking is needed.
Mayan numeration was base 4, 5, and not necessarily base 20. Cycles quickly emerged with 13 at the center, a dark number in many cases ... building 260. I want to study the happy numbers of the Maya,
George I. Sanchez, "Arithmetic in Maya", 1961, disclosed a hand abacus, 3 finger digits plus a zero on one hand, and three finger digits plus a zero on the second hand ... that allowed addition, subtraction, multiplication and division to be quickly worked out.
The deeper number theory hidden in calendar number statements were discussed by Floyd Lounsbury, a critical topic that seems not to cross your mind.
Best Regards to everyone that wish to give back modern Mayan their ancient math, as well as their ancient mathematical astronomy that included a yet to be decoded form of the Chinese Remainder Theorem ... a wonderful form of indeterminate equations that solved for solar and lunar eclipses .. and deeper number theory that calls out to be discussed here.