Currently grouping by month (or year) gives primacy to the first day of the
month/year as the cut-off point. Is there a way to arbitrarily select a
different cut-off point?

So for example my credit card statement may get generated on the 15th of
each month. For a particular card I may need to know whether my spending in
a particular statement month (which starts on the 15th and ends on the 14th
of the next month) has hit a certain amount (for rewards, or to fulfill
certain requirements).

Ideally I would be able to:-

SELECT
    year, month, account, sum(cost(position))
WHERE
    account ~ 'Liabilities:CreditCard:InstituteA:CardName'
GROUP BY year, MONTH(15)

or something of that sort.

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