Flying is certainly convenient if you've got luggage. Take a limousine bus from Kyoto station to Itami airport. There are free luggage carts you can use right in front of the bus stop. It's a very short walk to the terminal (ANA or JAL). Those airlines will check your bags through to your final international destination even when you have two separate tickets. So, when you get to Haneda there is no luggage to worry about. Only need to arrive one hour before check-in. If you buy that domestic ticket a month or so ahead of time, it's usually cheaper than a shinkansen ticket. Just presenting this as an option.