JR vs Shinkasen based on Itinerary

Below is our itinerary and I believe I have done a cost comparison and the single Shinkasen tickets would be cheaper but I would like someone to review this to see if I am correct.

Day 1: Arrive at HND. Travel to Shimbasi station in Tokyo
Day 2-3: Tokyo
Day 4: Tokyo to Kyoto Kiyacho Station Minami (Gion area)
Day 5-6: Kyoto
Day 7: Kyoto to Arayshima
Day 8: Kyoto to Osaka (Namba station final stop)
Day 9: Osaka to Mt. Koya
Day 10: Mt. Koya to Osaka
Day 11: Osaka to HND

The cost comparison I did was the following:

JR pass 7 day plus 1 additional single ride (excluding smaller metro costs) = 365
JR pass 14 days (but only using 8) = 372
Shinkasen single tickets = 305

Can someone please confirm if this is accurate? And if the JR pass is somehow the way to go, do we make all our seat reservations at the airport so we don't have to wait in line at each station in other cities? or do we still need to present something in Kyoto or Osaka to travel to other areas even if we have reserved our seats (for free)?

thank you so much for your help in advance
MH