H there!
It is possible to purchase as many rail passes as you need, but bear in mind that 2x7days costs around the same as 1x21 day pass. That said, lets take a look at your travel in blocks of rail pass validity:
Part 1 - Fukuoka to Tokyo
-
Hakata > Hiroshima: ¥8900, (69mins, 280km)
-
Hiroshima > Kobe(hyogo): ¥9210, (119mins, 304km)
-
Kobe(hyogo) > Osaka: ¥390, (25mins, 33km)
-
Osaka > Kyoto: ¥540, (29mins, 42km)
-
Kyoto > Nara: ¥690, (45mins, 41km)
-
Nara > Kyoto: ¥690, (44mins, 41km)
-
Kyoto > Kanazawa: ¥6910, (124mins, 224km)
-
Kanazawa > Takayama: ¥4380, (161mins, 148km)
-
Takayama > Minoota: ¥4380, (101mins, 109km)
-
Minoota > Gero: ¥2970, (50mins, 61km)
-
Gero > Minoota: ¥2970, (52mins, 61km)
-
Minoota > Nagoya: ¥950, (68mins, 54km)
-
Nagoya > Tokyo: ¥10780, (106mins, 366km)
TOTAL: ¥53760 for 13 legs
- 07 day rail pass (¥28,300) saving: ¥25460
- 14 day rail pass (¥45,100) saving: ¥8660
As you can see, you only do enough travel during the period of 2/4-30/4 to warrant a 14 day pass and must do an extra ¥3940 of JR travel to warrant a 21 day pass. This means that if you are set on this as your itinerary I recommend you should purchase JR tickets for this part of your journey unless you think you'll be doing more travel or need the flexibility to change your plans.
Part 2 - Around Tokyo
Assuming you do a return to Sapporo and fly out of Narita during this period, here are your costs:
-
Tokyo > Kamakura: ¥2100, (48mins, 51km)
-
Kamakura > Tokyo: ¥890, (58mins, 53km)
-
Tokyo > Nikko: ¥5630, (121mins, 150km)
-
Nikko > Tokyo: ¥5630, (117mins, 150km)
-
Tokyo > Minakami: ¥6050, (135mins, 164km)
-
Minakami > Tokyo: ¥6050, (135mins, 164km)
-
Tokyo > Odawara: ¥3840, (35mins, 83km)
-
Odawara > Tokyo: ¥1450, (36mins, 83km)
-
Tokyo > Sapporo(jr): ¥23570, (593mins, 1196km)
-
Sapporo(jr) > Tokyo: ¥23570, (551mins, 1196km)
-
Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
TOTAL: ¥81920 for 11 legs
- 07 day rail pass (¥28,300) saving: ¥53620
- 14 day rail pass (¥45,100) saving: ¥36820
As you can see you will make significant savings with a 7 or 14 day rail pass during this period. I can certainly recommend a 14 day pass, especially if you do the journey up to Hokkaido.
General Analysis
I think you have a good trip forming. Take care that your itinerary makes sense in terms of transfers (for example it makes more sense to visit Kanazawa before Takayama I think), and also be aware that unless you have specific things to do in both Gujo and Takayama you may be spending too much time in these locations. Overall I think you still have a huge amount of scope for adding more locations to your trip, such as exploring Kyushu, Shikoku and the sea of Japan coast in much more detail. Keep me posted with your plans as you develop them!
Costings
800,000 yen for 7.5 weeks roughly translates to ¥15,000 per day. Assuming that hotels, flights and internal transfers are paid for that will be a good sum of money to spend on sightseeing, and in many areas will be too much. You should expect to spend anything between 1000-2000 per daytime meal, spending around 1000-3000 in the evening for good value to normal restaurants. Of course, it is possible to eat for a lot more than this if you want to, especially if you like sake :). This leaves you with a decent budget of around 10,000 per day for sightseeing, entrance fees and miscellaneous transport, which I think is a very healthy budget and will not be needed most days. To give you an idea of range, on a shoestring you could aim to spend around 2000-5000 per day and still get a lot out of your trip.
Hope this helps!