There is some mathematical theory about this stuff. When you want to pick the best option within a set time frame, a super rough simplification would be to monitor the options for about a third of that timeframe just to learn what the range of options is, then after that you pick the first option that beats all the options you’ve seen before.
This site goes into that in much more detail and with the actual numbers instead of my rough estimation.
So one suggestion could be to take the last 10 days of the previous month as the learning period and then start paying out when the cost drops below the lowest cost in that timeframe.
One flaw of applying this logic is that this is meant for randomly distributed data points and of course that’s not exactly the case with gas prices. Applying it to gas prices might risk never seeing a better price. But they could always decide to in those cases just start the payout in the last week and take their losses. On average they would probably still save a whole lot of money by simply applying this trick.