JAL has limited services KIX-HND, so bear that in mind.
JL 220 06:40 - 07:40 (connecting to daytime US flights or pretty much elsewhere, but who will wake up for this?)
JL 224 14:45 - 15:50 (connecting to late afternoon Asia/US flights)
JL 228 21:20 - 22:25 (connecting to the night time Asia/US/Europe flights)

That said, Shinkansen to Shinagawa (next to last station just before Tokyo station), then a swift hop to the Keikyu line train will get you to HND in no time (Shinagawa to Haneda has 10 minutes frequency, journey takes around 25-30 minutes).
For luggage, get the seats at the last row (back end) of any train carriage, and the space behind the seats is ample space even for large suitcases.
Doing air transits from Kyoto will just waste your time and stress you more, and has less flexibility.
Unless, of course, you have Avios/United miles and can do the domestic flights at ridiculously cheap out of pocket costs. Then, I would vote for the Kansai (KIX) flights, with the benefits of a smoother connection out of Kyoto station.
*Note that at HND, you would still need to do the domestic to international connection landside.