We are both fit and have done a lot of travelling, two months in the States in a camper van and a 10-week trip to Canada and Europe in 2016 in a rental car and camper van.
It would be really good to know the best way to organise this trip because it has been a destination that we have wanted to go to for a long time.
I went to Japan for the first time this year, and had a great time as an independent traveller - mostly because it's so easy to get around on the excellent public transport system. Not that long ago, it would've been a lot more confusing as all the signage was in Japanese, but now there are English translations of everything and Google Maps has public transport integrated. With this in mind, a pair of travellers armed with the Japan Rail Pass can easily make their way around the country with a loose itinerary.
As I was only there for 10 days, I focused on exploring Tokyo. When I needed a break from the business of the city, I took a day trip to somewhere like Kamakura and breathed in the fresh air around the temples and seaside.
Since you're experienced independent travellers, I'd say you're more than capable of taking on Japan yourselves. When it comes to booking hotels, read lots of reviews and look for places that are close to train stations - I found location to be most important factor. Rooms can be small but you won't spend much time in them.
One thing I did find hard at times was the lack of English-speaking people - I got by with a translator app and a bit of pidgin Japanese, but it was helpful to meet up with a friend who spoke the language properly.
I imagine being on a tour would make things a little less "lost in translation" - plus you can learn a lot from a local guide and experience things you might not have found yourselves.
But you needn't choose between the two - you could start with a shorter tour through one area and go independent for the rest of the trip.
I walked a lot in Japan - there are so many little details to take in - so considering that, I'd suggest Walk Japan, which offers walking tours from two to 11 days. They range in difficulty level so you can choose one that works for you. The company was founded by academics so there's a strong focus on history and culture. Many include stays in traditional Japanese inns, which is something I wish I'd experienced.
Whatever you decide, I'm sure you'll have an amazing time. Eat as much as you can!