11 days in Japan - will the 7 day JR pass work for us?

We fly in and out of Kansai International Airport (KIX):
Day 1 (Tue 7/10): Kyoto (depart KIX for Kyoto around 8.30am)
Day 2 (Wed 8/10): Kyoto
Day 3 (Thu 9/10): Kyoto - Day trip: Magome-Tsumago hike
Day 4 (Fri 10/10): Takaragawa Onsen (Minakami)
Day 5 (Sat 11/10): Tokyo
Day 6 (Sun 12/10): Tokyo - Shimokitazawa & Shinjuku
Day 7 (Mon 13/10): Tokyo - Shibuya and Harajuku
Day 8 (Tue 14/10): Tokyo - Roppongi & Ginza & Tokyo Central
Day 9 (Wed 15/10): Tokyo to Osaka
Day 10 (Thu 16/10): Osaka – possible day trip to cycle the Kibi Plain (outside Okayama)?
Day 11 (Fri 17/10): Osaka - fly home!

I'm thinking we get a Kansai area rail pass to get us to Kyoto on Day 1 and just buy an all day bus ticket for Day 2.

Day 3 is a bit interesting. We need to get a train from Kyoto to Nakatsugawa, a bus to Magome, hike across to Tsumago, then a bus to Nagiso then rail back to Kyoto via Nagoya again. From my understanding the JR Pass does not include the Shinkansen Nozomi, therefore looking at the Hypedia website our best choice would be:

6.42am Kyoto - 7.33am Nagoya : SHINKANSEN HIKARI 506
8.07am Nagoya - 9.21am Nakatsugawa : JR Chuo Line Rapid
... bus to Magome ... hike to Tsumago ... bus to Nagiso ... 3.55pm Nagiso - 5.01pm Nagoya : LTD. EXP (WIDE VIEW) SHINANO 16
5.11pm Nagoya - 5.47pm Kyoto : SHINKANSEN HIKARI 477

If we activated a 7 day JR pass on Day 3 to the the day trip above, this should also get us from Tokyo to Osaka on Day 9, or would we have to leave before 6.42am to scrape in the 7 day limit???

Any advice would be much appreciated.