Would a 14 day pass be more economical?

Apologies in advance for what I assume is a frequent question here! I have been reviewing the information on Hyperdia with our itinerary but I just wanted to present the question here as well in case I have missed something important.

Our itinerary:
- 15 days - Tokyo for first 5 days (land in Tokyo evening of first day, planning to go to Kamakura day trip and possibly Hakone day trip) - then Hiroshima for 2 days - then Kyoto for 5 days (including Himeji, Osaka, Nara half day/day trips) - then back to Tokyo for 3 days (fly out 3rd day evening) - we are away from Tokyo for 8 days going to Hiroshima and coming back from Kyoto at the end (7 day pass wouldn't cover it)

I've been calculating and it looks like it could be pretty much equal if we do 7 day or 14 day pass. For the 7 day pass, we'd have to buy a separate ticket Tokyo to Kyoto (since the 7 day pass means we would either have to pay separately for Tokyo-Hiroshima or Kyoto-Tokyo).

Should we just get a 14 day pass? Thank you so much for any advice you may have!