>> We will go from Tokyo to Kyoto, is it better to have the hotel ship our large cases when we check out from Tokyo and just take backpacks on the train?
Yes. Depending on how long youm are staying in Kyoto, you could send luggage from Tokyo to Kyoto and to Osaka. Then maybe you just have one bag to carry from Kyoto to Osaka.
Get creative: ship from Kyoro to Osaka/Hiroshima, from Osaka to Hiroshima or departure airport. At some point you combine fresh clothing into one bag. used clothing to another bag and send that one to the airport.