On the hidden teachings suggestion - a book has recently been published on the history of English gardens with a chapter on Catholic gardens (shades of Mary, Mary, quite contrary). Here there is written evidence for cryptic plantings in the diary of an imprisoned Catholic, and what was encrypted, as might have been predicted, was the knowledge of Marian holy days, saint's days no longer celebrated, and practices associated with them, in other words, what is different from Protestantism, which the suggested meanings do not record.
Mathematically, the gifts build up as the sequence of triangular numbers, 1, 3, 6, 10...78, and the cumulative total as the sums of these numbers, 1,4,10,20...364, so the nearness to the number of days in a year, derived from the number of months, is an accident of number. If you draw out a table to show the gifts, especially one with the cumulative totals, there's a lot of mathematics, including square numbers, to be discovered. You could, of course, find the same things from a stack of baked bean tins... but not have so much fun.
Happy counting, Penny