Just type in a few of your intented routes in Hyperdia and you will see the regular prices. Pretty easy to figure out if you are saving. If your side trips are a bit longer you probably will. If you go south from Fukuoka those tickets get very pricy. Your Fukuoka-Toko ticket alone will be about ¥20k out of the ¥29k for the regular rail pass.

Don't buy the argument that for first class you will have less issues getting seats. That's hardly ever the case. And not an issue when you get your tickets a few days before. The only time I had a problem was when I travelled on a Sunday morning without making seat reservations. But even then I found a (regular) seat in the non-reserved car.

But when I travelled a few months ago I did appreciate the extra space and a little less crowded trains. On some of the trains the difference in seats is more significant than on others. I could care less about the towel you get in First.

And the difference for a 7day passs is "only" about $100 pp.