Dear Johanna,
Welcome to the Forum. Looking at your itinerary, I think you are planning a lovely nice trip. You will be in Japan during the Cherry blossom season and the weather in April is very well suited for traveling and sightseeing.
To answer your first question: Yes I think that in your circumstance it is very well worth going for the Green Pass. The greatest advantage is probably that you can travel in quiet with more space and extra luxury. During the Cherry Blossom season more people may be on the move, so it is a good time to use it.
Before your post I had not heard of the JR Full Moon pass, so it took some research to figure out.
In short, it is a pass aimed at married senior couples that together have the combined age of 88 or more. It can only be used for Green class (first class) cars on the JR and can be bought for a period of 5, 7 or 12 days for a price of ¥80,500 / ¥99,900 or ¥124,400 respectively (1 pass is enough for 1 couple). I must say that I really like the idea of this pass and it is available for Japanese couples too.
Compared the the JR-Pass it is still relatively expansive however. Here is a little comparison compared to the JR Green Class Pass. Please note that you have to buy one pass for each person.
7 Days ¥37,800 (or 75.600 for two / 5400 per person, per day)
14 Days ¥61,200 (122.400 for two / 4371 p.p.p.d)
21 Days ¥79,600 (159.200 for two / 3790p.p.p.d.)
For the Full moon pass this is ¥8050 / ¥7135 / ¥5183 p.p.p.d. for 5/7/12 days respectively.
For reference: the normal class rail pass cost
¥28,300/7 Days
¥45,100/14 Days
¥57,700/21 Days
It's a lot of numbers so I hope it is understandable, let me know if it is not clear in anyway.
Looking at your itinerary I have made a little oversight of what would make most sense it terms of value for money:
The first part I looked at was what would be best to cover with the JR-Pass and what options are available.
I would recommend a 14 day JR-Pass for your travel from the 29th of March to the 11th of April. This will cover all of your major traveling and also your journey from Narita Airport to Tokyo. For your local travel in the Kansai Area (Kyoto, Nara, Osaka and Kansai Airport) I would recommend buying single way tickets and use the local trains, they are very reasonable.
Kyoto --> Nara ¥690
Nara --> Osaka ¥ 780
Osaka --> Kansai Airport ¥ 1,060
Here are some additional tips for your itinerary:
Nagano is a very nice place to visit, if you are there for a day the Temple is the place to see first. The Temple consists of 3 areas, you can buy a ticket for the main temple only or the whole complex. From personal experience I think it is certainly worth it to visit all 3 areas. They show some remarkable history and art. Most of the time there is a free English guide available, who is very knowledgeable. If possible I would certainly ask them for a free tour.
When you are in Nagano you can also visit the Matsumoto Area, although you would probably need a day extra for this. The nature there is very beautiful and the Castle and various Onsen are worth a visit as well. You can read more regarding Matsumoto here http://wikitravel.org/en/Matsumoto
Takayama and Kanazawa are wonderful places to visit too, you simple can't go wrong here. My personal recommendation when people visit Kanazawa is always to visit the Castle plus its accompanying gardens and the Geisha district.
After Kanazawa you could consider going to Hiroshima for a day, I would recommend to visit the Peace museum, the memorial park and A-bomb dome. This can all be done in a single day even at a relaxed pace. One of the reasons why I would recommend this, are the impressions that the museum leaves you with, it displays the period of the atomic bombing of Hiroshima and the time after. It is hard to describe what happened there but seeing it all in the museum left me unable to talk for some time. Also making this extra stop would mean that you get most out of your JR-Pass.
You could plan this in by staying one day less in Kyoto (6 Nights is still a long time) or visiting Nara in a day trip. Nara is not a very big city so you can easily see it in a day.
7 Nights (or maybe 6) in Kyoto is quite a long time, if you would like to see something else while you are there, consider a day trip to Kobe. There are many things there worth to see and visit, such as it's China town and Sake breweries. Additionally if your JR Pass is till valid a day visit to Himeji to visit the Castle there is a possibility.
Let me know what you think and if I can assist you further in any way.
Kind Regards,
Daniel
PS: I can help you in your native language as well, assuming that you are Dutch.