KIX (Kansai International Airport) to Koyasan

Hi! I will go to Japan for 9D8N and exploring Kansai. I am planning to go to Koyasan directly after arriving at KIX. Estimated time of arrival is 8.15AM (with luggage, immigration, etc, maybe ready to go at 9AM). I will purchase JR Kansai Hiroshima for my trip, but since it only valid for 5 days, I am carefully planning when to activate it.

I have read that there's a bus directly from KIX (depart 10.10 AM) to Koyasan-okunoin mae (arrive 11.55 AM), costing 2000 yen. And I also read that Kansai Thru Pass will be cheaper for this trip since it includes bus cost around koyasan, and valid for 2 day. But I may only be able to spend time in koyasan until the end of the day, because I will depart from koyasan the next morning around 8 AM, and head to Nachisan waterfall.

I am planning to visit most of the tourist spot in koyasan so I am planning to purchase combination ticket of 2.000 yen, but I wonder if from 12 noon to the end of the day will be enough time to visit all the places? Also for this plan, I wonder how much of bus cost required for travelling within koyasan (1 day koyasan bus pass is 830 yen)? I read that Koyasan World Heritage Ticket (2860 yen) covers round ticket from Osaka, and discount admission for some tourist spot. But then, it will be useless since I will travel to Nachisan the next morning and not going back to Osaka.

This makes me confuse which is cheaper?
1. buying Kansai Thru Pass (meaning taking train from KIX) and Koyasan World Heritage Ticket, or
2. buying bus ticket from KIX, combination ticket (for admission of tourist spots in koyasan), and one day koyasan buss pass of 830 yen?

In addition, if buying Kansai Thru Pass is better, I wonder if the pass cover transportation to Nachisan the next day? (since it is valid for two days) Or better to activate the JR Kansai-Hiroshima from koyasan to Nachisan, and for the next 4 days. So I am very confuse which plan is the best for KIX-Koyasan-Nachisan trip.

Thanks a lot for reading and help!

Both the Kansai Thru Pass and the JR Kansai-Hiroshima pass do not cover buses between Koyasan and Nachisan waterfalls.

No good paying 4000 yen for the Thru Pass only to get to Koyasan. Pay the 2000 yen direct bus.

How do you get to Koya San the easiest from KIX?
Take a train to Namba?

I will arrive at 9:15 am at KIX but am confused about Express and Limited Express trains to Koya San

Really? You didn't read the first questioners post? It has the options in it.