Hi there,
Firstly, here's the price breakdown of your itinerary as mentioned:
- Kansai airport > Osaka: ¥2400, (51mins, 57km)
- Osaka > Kinosakionsen: ¥5450, (160mins, 183km)
- Kinosakionsen > Kyoto: ¥4710, (153mins, 158km)
- Kyoto > Shirahama: ¥6080, (176mins, 220km)
- Shirahama > Kyoto: ¥7170, (181mins, 220km)
- Kyoto > Nara: ¥690, (49mins, 41km)
- Nara > Kyoto: ¥690, (46mins, 41km)
- Kyoto > Tokyo: ¥13220, (161mins, 513km)
- Tokyo > Nagano: ¥7970, (105mins, 222km)
- Nagano > Kyoto: ¥10630, (228mins, 398km)
- Kyoto > Kansai airport: ¥3490, (79mins, 99km)
TOTAL: ¥62,500 for 11 legs
Looking at your dates, you'll be travelling for 17 days. There are certainly savings to be made here as even buying a 21 day at ¥57,700 you will make some saving over separate tickets.
As your Nara visit is probably not movable in the middle of your trip, I think it'll be most cost effective for you to buy a 14 day pass starting on the 6th and ending on the 19th. This would mean you would pay a total of: ¥50,990 (¥45,100 for 14 day pass + ¥5890 in separate tickets to and from the airport), a saving of ¥11,510 over individual tickets.
If you could move your Nara visit (and miss Omizutori), and shorten your stay in Tokyo then there are possibilities to save more by compressing more into a 7 day pass, but I think your itinerary is great (I especially like the idea of retreating to an Onsen to get over the initial jet lag!). It gives you a lot of space to explore, and if you have a specific thing you want to see in Japan you should certainly do it!
Hope this helps!