Hi,
According to your own schedule, a 7 day pass simply would not suffice.
If you go to everywhere you mention however, you still can get some good savings with a 14 day pass. Going to Tateyama is a little unclear though - there is a Tateyama on the Boso Peninsula in Chiba, but most think of the Tateyama Alpine Route. That would be a long and tough day trip.
You are right that travel during Golden Week is one of the most crowded times of the year. Getting a Green Pass is no guarantee of seating however. It's true that not as many people opt for the extra cost, however because of that there are far fewer Green seats. It gets to be something of a chicken and egg question. Whatever you decide, making as many seat reservations (which are free with the pass) would be a smart choice.
That said, in spite of the extra crowds and often higher costs for hotels, etc., travel during Golden Week also gives you some excellent opportunities that you don't have in other times of the year. The full bloom of the wisteria usually falls on the first week of May, and it is simply breathtaking to see. And you'll be within range of one of the best places in Japan to see it - the Ashikaga Flower Park in Tochigi. The season also is great to see the Hitachi Flower Park in Ibaraki, which has many kinds of beauty you will marvel at. Plus, it is also the season for the shibazakura in the Fuji 5 Lakes area.
If that isn't enough for you, during Golden Week is the Nanahana Festival in Iiyama, Nagano, also in Toyama not far from Tateyama is the Tonami Tulip Fair, and in Asago City Hyogo is the Shirai Omachi Fuji Park . If you are going to Japan during Golden Week, take advantage of the blessings.
You are right also that you can't use the JR Pass all the way to Fujiyoshida - you can take JR trains only up to Otsuki, and then you need to pay for the Fujikyu train for the rest of the way. Please be aware that the whole trip will take you 5½-6 hours.
