Fukuoka to Tokyo: There has to be a cheaper way

Help me please guys.

Due to some highly sentimental reasons, I could not pass up a visit to the Frog temple in Fukuoka for this trip. We’re coming from Hiroshima, so it seemed do-able to slot a little side quest in here for one night. I’ve just done a (very brief, very generic, very vague) Google Maps to preview the transport schedule of Fukuoka to my next destination in Tokyo, and I can see it is a five hour trip (which is fine) and an icy cold ¥230,00 (a lot less fine).

I’ve been in Kansai since arriving at the start of the month, and have made great use of stacked JR West rail passes to get around and I’ll be using the Kansai-Hiroshima pass to get down to Hiroshima for one night. Is something like this for Fukuoka or Tokyo that I can use to cut my commute’s cost down? I really prefer not to spend 230,00 on a train trip but the Frog Temple is a very cathartic, sentimental destination that I don’t want to miss.

Please help me work out the cheapest way to get back from Fukuoka to Tokyo.