Depending on what time your flight arrives in Tokyo and especially if you're in a lay flat seat, or how well you travel, you might consider the possibility of going straight to Kanazawa, Takayama or even Kyoto instead and staying your first night elsewhere than TYO. That way you'd eliminate an entire day of traveling to and checking into a hotel in Tokyo. If your flight arrives at Noon you could easily be in a different city by 5 pm. It may sound grueling but besides streamlining the schedule, I found it helps to adjust to the new time zone because you'll avoid napping/sleeping that'll screw up your inner clock.
I only spent a day in Fukoka and I enjoyed it but depending on the goal of your trip I don't know if it's worth going there when so much of your entire journey would be checking into a hotel one day and then out again just one or 2 days later. I was there on a Sunday though and it was pretty sleepy so I might not have the most brilliant perspective - it just seemed like a place I'd rather spend, say, 5 nights and really explore rather than a quick hit. I don't see it being as full of highlights as any of the other stops on your planned journey.