Might be a bit tedious, but I want back up for a point

When prepaying a charge that spans multiple accounting periods, should you prepay to the end of the period, or the calender month?

Not sure exactly what you mean.

Our periods are months. We always prepay on a monthly basis and makes no difference whether its a month end or year end.

Accounting period.
But time, effort and materiality may make ‘calendar month’ the preferred option.
I.e. it is easier to divide an annual charge by 12, than to work out the amount prepaid when the accounting peiod might end on ‘the last Saturday in the month’, for example. 
It also equalises the charge when you have 4 and 5 weeks in a ‘month’ (not that that is particularly valid).
A long as you are consistent, it shouldn’t matter too much.