Travelling Around by Train

we are arriving in Osaka on the 31 March and departing on the 16 April - 17 days

we plan to travel from Osaka to Hiroshima to Fukuoka to Kyoto to Tokyo to Sendai - as much as possible

if I choose the Green card the 14 days is £453 and the 21 is £589 - difference is £136 per person

I am either 3 short or pay for 4 days extra

is it worth it? paying the extra for 21 days?

any assistance would be great

thank you