Koyasan and Kumano Sanzan itinerary?

I'm trying to figure out a very rough itinerary for travelling to Koyasan and the Kumano Sanzan from Kyoto or Osaka. Ideally I'd like to avoid having to go the big JR roundabout of the peninsula twice, if at all possible, so I was thinking:

Day 1) go from Kyoto/Osaka to Koyasan using the 2-day pass, sightseeing, stay overnight at Koyasan Day 2) sightseeing, go to Kii-Katsuura, stay overnight at Kii-Katsuura Day 3) Do the Kumano Sanzan Circuit (http://www.kumano-travel.com/index/en/action_ContentsDetail_PlanDetail...), then back to Kyoto/Osaka.

The big question is how to best do the travel to Kii-Katsuura from Koyasan. I'd like to not have to go back to Hashimoto-Wakayama-Kuroshio line to Kii-Katsuura, since that'll have to be the train I take back if I understand correctly.

Also, is there anything else I absolutely need to see while I'm in that area? Maybe the Sesshakannokura Shrine in Shingu?

you may check this thread for inspiration: https://www.japan-guide.com/forum/quereadisplay.html?0+160337