Mate really? I've always achieved as much rest as possible pre flight and during the flight where possible BUT how can you not be fatigued at the time of your circadian low body clock? Im-bloody-possible.
I know you mention that you have but you've obviously not done long haul overnight sectors......
It's impossible not to be tired. You do know being tired at that time is the same a being DRUNK to in excess of the .05 limit for driving....proven fact.
Personally after having done multi sector day flights causing tiredness versus overnight long haul jet lag I find the overnight to be more dangerous....our bodies just weren't designed to stay awake all night long AND be alert to land at 5:30 am
If you are different then lucky you...
Personally I do whatever I can to keep the operation safe and simple after being awake all night.