JR pass 14 days or 21 days/Itinerary suggestions

Hiya, me and my friend are visiting Japan first time in October. However our itinerary is as follows and not sure if we can buy the 14 days pass + another rail pass (which one?)

13 Oct: Transport Haneda airport to Tokyo
PM in Tokyo (Overnight cheap accommodation)

14 Oct : Full Day Tokyo sightseeing (Ueno park + anything else)
O/N cheap accommodation

This is where the issue is
15th - 19th : Transport to Narita as we go to Bali & back (long story:))

20 Oct- AM Transport Narita to Kumakara (sightseeing + O/N cheap accommodation)

21 Oct - AM Transport Kumakara to Mount Fuji (O/N in a mountain view/Hot springs accommodation)

22 Oct - AM Transport Mount Fuji to Kyoto
23 Oct - Kyoto (sightseeing + O/N cheap accommodation)
24 Oct - Kyoto (sightseeing + O/N cheap accommodation)

25 Oct - AM Transport to Mount Koya (read that there is another pass to buy) (sightseeing + O/N stay in temple accommodation)

26th Oct - AM Transport to Osaka (sightseeing + O/N cheap accommodation)

27th Oct - Free day
PM Transport to Narita airport

28th Oct - AM flight departure to LHR

Any suggestions please (only interested in ancient/sacred cultural mystical sites) ....thanks much.