OneTimeOffGuy, the responses to your plan(s) are a genuine reply "No way". Terrible and meaningless waste of time, and money. Hakone is one of the most overdeveloped tourist traps in the whole of Japan and with just a few hours thats all you will catch a fleeting glimpse of. Underneath the tat there is still charm and a reward for taking the time to discover it.
Skip Hakone this time, and the one night in Kyoto too unless you just want to experience the Shinkansen train ride. If you insist on Kyoto you might extend your time there by flying back direct to NRT to connect with your onward travel. Connecting flights from ITM into NRT are fewer than into HND but there are some.