It's awkward, but your 11:00 is someone else's 3 am. I have considered having production happen at a random time within a given 6 hour period during the day. But then you can't plan so well, or log on at a predictable time, etc. etc.
It would be cool if people could trigger their own production whenever they log on, if they're due for one. Oh my god, that would take forever to rewrite. I did not just say that.
The universal 4 a day is fundamental to play. You can plan attacks by them, execute massive trades, etc. With them being 6 hours apart, regardless of timezone, you ought to be able to hit 2 fairly comfortably, and 3 isn't unreasonable. All 4 in one day does take effort, but might be possible for some.