Travel flight plan from US to HND

Traveling from Texas to Tokyo. Is it better to maximize time and reduce jet lag to take a 1 am flight out of LAX and land at 4:45 am

Or

Take one of the cheaper flights that lands around 2-5pm

Almost all of the flights leaving Texas are early morning flights. I feel like it would be hard to sleep on the flight over as it would be “day time” and then landing in the afternoon and being exhausted. The red eye would leave Texas at 9 pm, layover in LAX, be easy to sleep and would essentially land in the morning and start the day running. I can’t believe there aren’t more red eyes.

P.S. looking to stay in Ginza. If you have any hotel recommendations I’d love to hear. Under $500 a night.