In the last ten nights of Ramadan this city eats at hours that suit us exactly, and our orders roughly treble.
What we do about it is the opposite of what people expect. We cut the menu rather than extend it. About half the items come off the site for those ten nights, leaving the things that can be cooked quickly and consistently by four tired people, and the hourly caps go down rather than up.
The result is that a Ramadan order arrives in the hour it was ordered for. The alternative, which we tried in our first year, is accepting everything and delivering half of it late and cold, after which a good number of those customers never come back.
We say all of this on the site in the week before, so nobody discovers it at eleven at night.