Will this Itinerary work?

Hiya, me and my friend are visiting Japan first time in October. However our itinerary is as follows and i have asked the question already regarding the JR pass but have posted here the same question to enquire if this itinerary makes sense and if anyone has suggestions as we are just about to start booking...(only interested in ancient/sacred cultural mystical sites). thank you

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

.thanks much.