What time of year will you be going? Depending on dates, there may be a sumo tournament at the Kokugikan. Since you are planning a visit to the Edo-Tokyo Museum right next door, a couple of hours seeing some matches might be interesting. Even if no sumo, the E-T makes a fine use of a few hours. The sumo museum, which is in the basement of the arena, is small and will only take a few minutes to see.
Your Day 1 could be a little more efficient. The river cruise and Hama Rikyu are better in the morning so I agree with the suggestion to take the cruise FROM H-K up TO Asakusa. The temple at Asakusa won't take all that long but there is plenty to see in the surrounding old neighborhoods and the Nakamise Arcade. (I actually did the cruise and garden in the direction you propose during my first visit but I was staying in Asakusa and just walked to the boat dock in the morning.)
I like your proposed sites to see in Kyoto but you can quite easily see them on your own, avoiding the whirlwind tour groups. Get a day bus pass at the transit office just outside the Karasuma exit of Kyoto Station and use buses #100, 101 or 102 to ride the tourist loop, getting on and off at the major sites. Grab a cab when you are tired or finished for the day. You will find them at every tourist venue. Take a brochure from your hotel and just point to it when you are ready to call it a day.