EVA Premium Economy is the best flight experience I have ever had. I am 1.98m tall (that's 6'6" for you Americans). Much better than Singapore Air! I flew once on EVA's business class and it wasn't worth the money IMHO. EVA stops in Taiwan.
Besides what everyone else said, I offer that it's much better to leave at night, sleep as much as you can on the cross-Pacific flight, arrive at night, and go immediately to a hotel room for (say) 6+ hours, then continue on during the day. No, you don't have to get your bags at that stopover - just buy a ticket with an 11-hour layover. When we do this to go to Bali in this way, we have barely any jet lag.
Going West-East is more difficult though, as others have said.
- Bill