I just had a very similar situation. JAX CLT LAX BNE ADL KGC.

In short, I stayed up for the two domestic legs.

Flight left well after midnight EST...

Fell asleep almost immediately after takeoff for the TPAC leg. Long flight 13 hours and change...slept for all but two of those hours. Arrived 6:50 am. Didn't nap at all on day 1. Avoided alcohol (Drank caffeine!).

I wasn't jet lagged AT ALL.

That said, the way back was another story...took 4 days to get over it