Regional v JR pass

Hi team. Travelling to Japan in Oct/Nov to walk Minchinoku trail. First, we want to do part of the Nakasendo trail, hop on hop off, and visit Koyasan. Flyng into Tokyo. My questiosn is, is there a pass, JR or regional, durataion about 7 days, that would encompass Kii valley and Koyasan? I know that part of Koyasan rail trip is private and therefore not covered by any passes. I am anticipating needing to buy separate shinkansen tickets for trip north Tokyo to Hachinohe, and also from Tokyo to Nagoya to start Nakasendo. Advice welcome! Othwewise, I coud get JR railass and use it from Tokyo to Nagoya to Koyasan to Hachinohe, all within 7 days, but it is only a marginal saving. Thanks!