Hi Paul!
Normally a 7 day pass makes sense if you do a return trip between Tokyo and Kyoto. As you're planning on doing a lot more travel than that I can certainly recommend a 7 day JR Pass over normal JR tickets.
Here is a cost breakdown for you to find out how much you will save:
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Narita airport terminal 1 > Tokyo: ¥3,140 (62mins, 79km)
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Tokyo > Kyoto: ¥13,020 (164mins, 513km)
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Kyoto > Kobe(hyogo): ¥3,240 (54mins, 75km)
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Kobe(hyogo) > Hiroshima: ¥10,580 (129mins, 378km)
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Hiroshima > Narita airport terminal 1: ¥19,940 (369mins, 973km)
JR ticket cost: ¥49,920 for 5 legs
Once you have purchased your JR Pass I'm afraid you cannot upgrade/downgrade, and so if you have a standard class rail pass and want to use the Green Car you will have to pay the full green car seat price (although the basic line price will be covered).
I hope this helps!