Best rail pass to buy - West Japan and Kyushu

Hi,

I've planned a trip to Japan in a couple of weeks, and am looking to travel around West and South Japan.
I've searched online for the best way to do this and I'm not totally sure, my itinerary is as follows:

Day 1,2,3,4 - Kyoto
Day 4,5 - Nara
Day 5,6,7 - Osaka

For the first week I'd be staying relatively local so wouldn't be looking to purchase a rail pass. Week 2 is where I'm unsure

Day 7,8 - Himeji
Day 8,9 - Fukuyama
Day 9,10 - Hiroshima
Day 10,11 - Miyajima
Day 11,12,13 - Nagasaki
Day 13, 14 - Fukuoka

Looking online it seems I have 2 options: JR Sanyo Sanin (7 days, 19,000yen) or JR Setouchi (5 days, 17,000yen).

With the exception of Nagasaki (which I will likely travel to by bus from Fukuoka, having travelled there by train from Miyajima/Hiroshima) all of my stops seem to be covered.
Can anyone advise which pass may be best to purchase - or if a pass would be financially worthwhile at all?
I'm leaning towards JR Setouchi as it seems to cover my destinations with the exception of Nagasaki.
Also, would the 5 day pass be sufficient time to cover days 7-11?

Thanks in advance,
David