S.K.
My husband and I spent a week in London and 2 weeks in Rome when our daughter was six months, so I know exactly what you're planning for! The good news is, at 4 months she is still sleeping quite a bit and isn't really mobile so she won't be wiggling much during the long flight. Our flight was closer to nine hours but Chloe did great! No tears at all!
I breastfed her during takeoff and landing to keep her swallowing so her ears wouldn't bother her (a bottle works well too), we took turns walking up and down the aisles a few times when she got wiggly to give her a change of scenery, and we packed a few of her favorite toys and snacks to enterain her with. Since your baby won't be eating solids yet, a few of her favorite toys/ stuffed animals would probably be fine. Honestly though, she slept much of the trip, I think due to the movement and noise of the plane.
We also asked for the bulkhead seating, not sure if they have that to Hawaii, but worth asking about. It had a platform that came down from the wall that a foam box buckled to, making a little bassinet that we could lay her down in while she slept to give ourselves a break. I called the airline and they hooked it up! It also gives you more legroom, more space for that diaper bag and is a huge plus for tall parents!
Another tip is to dress her in several layers and bring an extra blanket so that you can keep her warm on the plane and cool once you get off.
As far as the time change, we noticed that with all the commotion and excitement of traveling she stayed up later than usual and slept longer once we went to bed, so it didn't take long to adjust her schedule. Keeping the shades open while she's napping and closed when you guys go to sleep might help. We tried to ply with her when she started to get tired to keep her up a little longer but woke her when we got up in the morning, so she switched over pretty quickly.
Have fun! This is a great time to travel with a new baby and you deserve the rest! :)