Personally I will take plane to ITM followed by bus, regardless if the paid by miles or cash (actually it may be wiser to pay for the ticket as it's only 10K Yen for domestic Yokoso / Welcome to Japan fare, YMMV)

If you take HND-ITM-Kyoto, you only need to move your luggage from HND arrival to custom, then re-check the bags for the domestic flight. Upon arrival to ITM, take the direct bus to Kyoto and there are ample of space for your luggage.

On the other hand, if you take train, you have to get the luggage on Keikyu Line (which is, of course, peak hour), followed by Shinkansen to Kyoto, that you have to pull the luggage all the way and Shinkansen is not particular known as luggage friendly.