Getting from Koya-san to Kii-Katsuura?

Ultimately I’m trying to get from a temple stay in Koya-san to Nachi Falls and, currently, have most of a day blocked out for the long journey through south-eastern Wakayama to accommodations in Kii-Katsuura. I’m considering adding an overnight stop somewhere in between, just because that journey seems a little too long and I love the mountains/natural landscape of the region. Any recommendations or perhaps a better route?