I don't think the famous "bamboo forest" is worth going to at all (I studiously avoid it when I go to Arashiyama), and most Japan experts tend to pan it. I think there are nicer alternatives, and if you spend some time researching the subject you will likely find them. It is selfish of me, but I often don't promote some of my most favorite places by naming them, because I don't want them to become future tourist magnets... I figure if people care enough they will find them (the information is out there), and if they don't, then they can just settle for the same-old same-old. But anyway, if you are in Japan for 50 days you will see some nice bamboo groves. Just keep your eyes and your minds open. I really think that a lot of tourists who are fixated on must-see sites don't take the time to appreciate all of the wonderful things that they pass by on the way to those sites. So many of my peak experiences in Japan have been serendipitous.
Generally speaking, the earlier in the day the better as far as popular sites go. One reason is that tour buses tend to not start arriving at places until around midmorning. Tour buses dump huge volumes of people on sites. But in general, tourists typically like to get a somewhat late start. Of course you need to keep the opening hours of any sites you want to visit in mind. Many shrines are open dawn to dusk (and some never close), and some temples have nice grounds that are always open. At the time of year you are going, you are going to have less trouble with crowds than if you were to go at busier times, and you might find even some popular spots to be not very crowded. But you're never going to find places like Kiyomizudera or Ginkakuji deserted. I would say just don't worry about it, but be sure to go to some places besides the must-see spots. And stay away from top-ten sites on the weekends.
The pros and cons of JR passes and other transit passes are numerous (and many of them are often overlooked because people tend to focus only on whether a pass will save them money for a preplanned, fixed itinerary). The Nozomi-Mizuho thing is a fairly major issue but not a deal-breaker for me, but off the top of my head I can't come up with a complete list of "cons." One real negative for me is that when I have a JR pass, to a large extent I tend to focus most of my attention on sites that I can get to by JR, and am reluctant to spend money on non-JR transit. The result is that there are a lot of good places in Japan that I have never been to. Lots and lots of places in Japan are not served by JR, and although I will often spend money on non-JR transit, having a JR pass is still a dis-incentive to doing so, especially with the arm-and-a-leg pricing on the JR pass these days. A more minor issue is that you have to physically pick up the pass once you get to Japan, and this is a chore that can be time-consuming. (In particular, if you want to pick the pass up at an airport or in Tokyo, be prepared for a very exasperating wait in line.)
Even before the huge price increase on the nationwide pass, there were some knowledgeable Japan travelers who disliked the JR pass because of various constraints that I don't have the time to get into (possibly they might weigh in if they are reading this) and because in many cases it didn't save much if any money. Again, I think that to merely compare pass prices with single-ticket prices for a fixed itinerary can be simple-minded, especially for people who have plenty of time and seriously want to experience "the real Japan." (There is nothing wrong with following a standard fixed itinerary, and for many newcomers it is the right thing to do, but people who want "off the beaten path" experiences will need to spend a lot more planning time in order to accomplish that goal, and those people are more likely to get value, beyond simple monetary savings, from a pass.) So to be honest, I can't see too much value in your fare calculator comparison, plus I just don't think in euros :) And I didn't try to figure out your calculation for number of tickets. You can use the JR pass without tickets only if you ride in unreserved seats, and some trains don't have them, plus when you have the pass you will tend to make reservations "just to be on the safe side," which is for me actually a downside as much as a "pro," because in many cases unreserved seating is actually a better choice. I don't know that having a JR pass would reduce the complexity of your trip. The planning you need to do to get an enjoyable trip (not just a lot of pointless train-riding) that gets more than "face value" from a pass is considerable. Of course, there is convenience in having a pass even if you don't use it very much, but the "wasted" money could really be put to better use.
Although a 21-day pass worked great for me on my last 30-day trip, for a different trip I might not get one (I would likely get some other pass or combination of passes), but I doubt if I would ever get two 21-day passes for a 50-day trip. A hugely expensive nationwide JR pass basically encourages you to do enough travel to recoup the cost, and I can sustain that for 21 days (like I said, I still had plenty of "easy" days on my last trip) but I think I would be hard-pressed to do that for 42 days.
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