Delta all the way. I went Shannon to JFK to LA to Honolulu in 2001. On return journey, we went Honolulu to LA to Vegas (for a week!!!!) and then Vegas to Atlanta to Shannon.
The stopovers only lasted a few hours each. We picked up our luggage in JFK and resubmitted it. We didn't have to pick it up in LA. This might have changed since 9/11. Our entire journey in real time from Ireland to Honolulu including stopovers was over 23 hours. Thankfully, it was night time locally when we arrived and we hit the sack.
For the purpose of the trip, I joined Delta Airmiles. We got bumped up on one of the flights and we didn;t need to queue for ANY of the flights.