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Thanks for the info, so many options!
Re bikes - we are open to options, we did a similar thing in Sicily, flew with bike boxes and left them in Palermo while traveling around. Also happy to use cardboard boxes if we start and finish in different places.
Because of the bike bag situation on trains, I also thought it might be best to fly to Kyoto, leave boxes there, do a loop, then pack them up for a train journey to Tokyo where we would do non-bike stuff before flying out.
I did a quick month long tour a couple of years ago, flew in to Tokyo and rode to Nagasaki and back. Camping wise, I mostly wild camped and given that public facilities (bathrooms, even outdoor showers at coastal locations) are amazing it still felt pretty cushy even on rainy days I always found a quite covered public rest area to stay dry in. There's a really useful google 'mymaps' out there that has the locations/details of all the road houses, onsens and free campsite sin the country that you can load straight onto a GPS. Destinations wise I really enjoyed the Irago Peninsula, the five lakes route around Mt. Fuji, the Shimanami Kaido (of course) and some of the mountainous riding in Gifu. I think Lake Biwa would be nice in better weather but I had several very gray days then. How are you travelling with your bikes? I found it super easy to fly in to Tokyo with my bike in a bag get the train in from the airport and then leave the bag at the hostel for the month that I travelled then simply stay there another night before departing and pack the bike up again. Have fun, I'd go back to tour again in a heartbeat!