The itinerary looks great. An interesting mix of lots of different parts of Japan (frankly, I'm a little envious...)
Firstly, here's an approximate cost breakdown for your journey. I didn't include any airport hops as you didn't mention these above. I also only included your main legs. You will get use from the JR Pass in Tokyo if you use the Yamanote line, but I wasn't sure if you were planning on that or the metro so left them out.
- Tokyo > Otsuk (for FujiQ): ¥2660, (84mins, 87km)
- Otsuki > Tokyo: ¥1450, (100mins, 87km)
- Tokyo > Takayama: ¥14000, (275mins, 532km)
- Takayama > Kyoto: ¥9380, (191mins, 314km)
- Kyoto > Hiroshima: ¥10590, (109mins, 380km)
- Hiroshima > Miyajimaguchi: ¥400, (26mins, 21km)
- Miyajimaguchi > Osaka: ¥10540, (148mins, 367km)
- Osaka > Kiitanabe (for kawayu onsen): ¥5090, (140mins, 175km)
- Kiitanabe > Osaka: ¥4930, (133mins, 167km)
- Osaka > Nara: ¥780, (62mins, 48km)
- Nara > Osaka: ¥780, (55mins, 48km)
- Osaka > Tokyo: ¥11850, (194mins, 556km on Sunrise Seto sleeper)
TOTAL: ¥72450 for 12 legs
There is room for lots of saving here! At ¥28,300, a 7 day will certainly save money, but is it cheaper to get a 14 day pass at ¥45,100 or just add separate tickets?
For the days outside your 7 day rail pass, your costs in separate tickets comes to about ¥18,110, which is more than the ¥16,800 difference between the 7 and 14 day rail passes. This means you'll make a small saving of ¥1310 with a 14 day pass than with a 7 day pass and separate tickets. With the added flexibility, it's fairly clear that the 14 day rail pass offers the best value.
Also, with a 14 day, you'll probably cover other trips too around Tokyo that I didn't include, and may be able to include airport hops if you're arriving by plane.
Recommendation: 14 day rail pass
Hope this helps!
P.S. Loved learning about Kawayu Onsen! I've never been, but it has been added as one of the places to go on my next visit! (nice saving with the rail pass too!)