14 day JR pass or 21 day?

Hi,

We are looking forward to our Japan holiday this April!!
But we are not sure what is cheaper: a 14 day JR pass or a 21 day pass?
This is our itinerary:

Day 1: arrive Tokyo Narita -> Tokyo
Day 2 - 6: Tokyo (with a daytrip to Nikko and Disney sea)
Day 7: Tokyo -> Minakami
Day 8: Minakami -> Kyoto
Day 9 - 12: Kyoto (with a daytrip to Nara)
Day 13: Kyoto -> Himeji -> Hiroshima
Day 14-16: Hiroshima (with a daytrip to Miyajima and maybe rent a car for one day)
Day 17: Hiroshima -> Tadanoumi (ferry to Okunoshima) -> Osaka
Day 18 -19 : Osaka
Day 20: Osaka -> Tokyo
Day 21: Tokyo -> Mt Fuji -> Tokyo
Day 22: Tokyo -> Narita

We were thinking about taking a limousine bus the last day back to the airport.
Is it worth taking a 21 day day JR pass while we are spending the first 6 days in Tokyo?
When we will take a 14 day JR pass, which day will be the best date to start the pass?

Thank you so much for helping!

Cheers from the Netherlands,
Bastiaan & Rosanne