2 days in Kumano in between Kyoto and Koya

Hello everyone,

There has been a couple of posts over 2-day trips in Kumano, but not specifically in that sequencing (I think!) so apologies if I have missed them.
I am planning a trip around early September and would like to travel to Kumano in between Kyoto and Koya (as we are planning to go to Shikoku thereafter through Wakayama).
Does it seem doable to do the below??

Day 1:
- Morning: Kyoto to Nachi (arrive ~2pm)
- afternoon: Visit Nachi Taisha
- Evening: spend evening at Shingu and visit Hayatama Taisha (or better to try and go directly to Yunomine Onsen and perhaps "skip" Hayatama Taisha?)

Day 2:
- Morning travel to Yunomine Onsen and drop bags
- Afternoon Vist Hongu Taisha and walk around trail loop (or mix bus+walk)
http://www2.tb-kumano.jp/en/kumano-kodo/pdf/Kumano-Kodo-Hongu-Area-Map...
- Evening: night in Yunomine onsen

Day 3:
- bus to Koyasan: There seem to be a limited access bus (bottom of the attached link) but somehow the website does not seem to work so well - has anyone used it and knows how long it takes?
http://www.tb-kumano.jp/en/transport/hongu-koyasan-access/

Appreciate your thoughts on the above and any ideas! Do not that we have already booked Koyasan accommodation :)

Thank you!

Here are some pickups from Jaran's Top 30 in Wakayama in September. Some are doubling.

4.4 367 830-1630 2h Nachi Taisha http://www.jalan.net/kankou/spt_30421ag2130013132/
4.5 823 1h Nachi no Otaki http://www.jalan.net/kankou/spt_guide000000172017/
4.5 401 830-1630 2h Okunoin http://www.jalan.net/kankou/spt_guide000000172065/
4.5 343 3h Koyasan http://www.jalan.net/kankou/spt_30344ab2010002963/
4.5 342 830-1700 1h Koyasan Kongobuji http://www.jalan.net/kankou/spt_30344ag2130010978/
4.4 400 1h Hongu Taisha http://www.jalan.net/kankou/spt_30426ag2130013133/
4.4 367 830-1630 2h Nachi Taisha http://www.jalan.net/kankou/spt_30421ag2130013132/
4.4 265 1h Nachi no Taki http://www.jalan.net/kankou/spt_30421ab2042042932/
4.3 173 3h Kumano Kodo http://www.jalan.net/kankou/spt_30206af2160017414/
4.4 137 3h Yunomine Onsen http://www.jalan.net/kankou/spt_30426cd2110078466/
4.2 215 30m Hayatama Taisha http://www.jalan.net/kankou/spt_30207ag2130010959/

I could estimate the needed times for the below.

3h Nachi
6h Koyasan
7h Hongu
30m Shingu

I first thought of via Gojo. You would not have to rush to Yunomine on Day 1.

D1 Kyoto 836-1257 Kii-Katsuura 1310-1335 Nachisan 1710-1727 Nachi 1733-1751 Shingu/Hayatama
http://www.kumakou.co.jp/bus/jikoku_item_9.html

D2 Shingu 840-949 Yunomine Onsen
http://www.kumakou.co.jp/bus/jikoku_item_7.html

D3 Yunomine Onsen 856-1257 Gojo 1303-1416 Koyasan
http://www.narakotsu.co.jp/rosen/yagi-shingu/totsukawa-timetable.html

D4 Koysan 935-1309 Wakayama Port 1340-1555 Tokushima Port
http://www.nankai-ferry.co.jp/timetable/kudari.html

In the opposite direction, you would have more time in Koyasan, but lose the time in Hongu.

D1 Sanjo 852-1130 Koyasan
D2 Koyasan 841-1022 Gojo 1031-1434 Yunomine Onsen
D3 Yunomine Onsen 850-959 Shingu 1125-1146 Nachi 1218-1235 Nachsan 1550-1615 Katsuura
D4 Kii-Katsuura 853-1309 Wakayama Port 1340-1555 Tokushima Port

Then, I found a dedicated site for Seichi Junrei Bus. It is faster than the route via Gojo. You could drop at Okunoin before Koysan.
http://seichijunrei-bus.jp/maptime_us.html

Yunomine Onsen 831-1220 Koyasan

Koyasan 955-1423 Yunomine Onsen