Hi there!
I think the idea to base yourself out of Kyoto makes a lot of sense - there's nothing worse than lugging baggage around while you are on holiday.
Looking at your itinerary without Hiroshima, I think I'd recommend purchasing a Haruka + ICOCA on arrival into Kansai to give you transport into Kyoto and some prepaid travel on the metro/JR with ICOCA card. After this, within Kansai it would really depend on the amount of travel you do as to whether a regional pass makes sense, but you should plan on purchasing single tickets up to Tokyo.
If you do include Hiroshima/Miyajima, then the situation gets a little more clear. Here are your rough costs:
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Kansai airport > Kyoto: ¥3,690 (75mins, 99km)
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Kyoto > Hiroshima: ¥10,990 (112mins, 380km)
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Hiroshima > Kyoto: ¥10,990 (126mins, 380km)
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Kyoto > Osaka: ¥540 (28mins, 42km)
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Osaka > Kyoto: ¥540 (29mins, 42km)
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Kyoto > Nara: ¥690 (44mins, 41km)
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Nara > Kyoto: ¥690 (44mins, 41km)
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Kyoto > Tokyo: ¥13,420 (161mins, 513km)
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Tokyo > Otsuki: ¥2,860 (85mins, 87km)
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Otsuki > Tokyo: ¥2,860 (76mins, 87km)
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Tokyo > Narita airport terminal 1: ¥3,140 (58mins, 79km)
JR ticket cost: ¥50,410 for 11 legs
As you can see, with Hiroshima a 14 day pass becomes a good choice. In addition to the savings you'll also have the flexibility to change plans and use the rail pass within Tokyo.
Please note that for Mt Fuji I have assumed you'll go to Kawaguchiko. The JR Pass will take you as far as Otsuki. From here you should use the non-JR Fujikyu lines up to Kawaguchiko itself (¥1110 each way).
On balance, if you include Hiroshima, a 14 day pass is a good idea. However if you do not include this leg, or are very firm in your plans, then a 14 day pass may not be the best choice.
Hope this helps!
