I admit being a slow traveler, but some of your days seem to be crazy busy to me.
Apart from tools the other point to consider with care is parking. There is no such thing as free parking (except rural places). So you need hotels with free parking or find a public parking lot and pay.
Specially in Koyasan, make sure the monastery you chose has parking or can tell you where to park. The village is small!
April 5: Osaka [Osaka Castle, Shinsekai, Dotonbori] donft be disappointed at Osaka castle.
Why not go directly from KIX to Koyasan and have an Osaka day later in your trip while staying in Kyoto? ( less change of hotels) and your win a bit of time that I think you dearly need over the next stretch of your trip.
April 6: [Road Trip] Osaka - Koyasan (sleep in a temple)
April 7: [Road Trip] Koyasan - Nara - Kobe - Arima (sleep in Onsen Ryokan in Arima)This day sounds crazy busy to me. Calculate that you need at least 24 h in Koyasan to really take it in.
Nara city in itself easily requires a full day (or more) and if you want to enjoy your onsen ryokan experience in Aroma onsen youfll need to plan to be there latest around 17:00 I time for Checkin prior to dinner.
I would do a area as a day trip from Kyoto by train, and get directly from Koyasan through Kobe to Arima onsen.
April 8: [Road Trip] Arima - Ritsurin Gardens - (Takamatsu Port) - Naoshima - Benesse (Sleep Naoshima)Benesse house is very popular so I hope you already got your reservation.
Do you want to see the art and museums on Naoshima? If yes, I think you donft have enough time as youfll arrive in the late afternoon assuming that youfll take the car ferry at 15:35 Museums will be likely closed by the time you get there.
You could aim for the ferry at 12:40, but that hardly gives you any time to drive to Takamatsu and see the superb garden. I would need 1,5 h minimum for the garden. And still doesnft give you that much time on Naoshima. Maybe just one museum. Or a round ride to see some of the open air art? Youfll need to stop at some time for things such as lunch!
https://www.shikokukisen.com/instant/#route01April 9: [Road Trip] Naoshima - Teshima - (Uno Port) - Kurashiki - Korakuen (Okayama) - Himeji - KyotoAre you sure there are any CAR ferries between Naoshima and Teshima? I canft find any. (But havenft spent hours on it searching for it. ) what I find is a pedestrian only ferry that runs only certain days of the week. So you would need to do Naoshima -Teshima- Naoshima and THEN back to Honshu. You should have enough time to see a Teshima (but as discussed above you donft seem to have enough time for Naoshima) but no time for any of the other places.
Even if we delete a Teshima from this day and you depart Naoshima directly after breakfast, Kurashiki, Korakuen and Himeji castle all in one day coming from Naoshima already seems to be a stretch. Consider that attractions in Japan close early (generally around 17:00) and it gets dark early. For Himeji castle I am told there can be long queues to get tickets.
https://www.shikokukisen.com/instant/#route04So summarizing I think you need to add likely 2-3 days to this part of the trip if you really want to do the places you visit some justice.
April 10: Kyoto
April 11: Kyoto
April 12: Kyoto
April 13: Day-trip to Ryokan just outside of Kyoto why in the middle of your stay in Kyoto one day in a ryokan? Why not at the end/ beginning or in a totally different place? Just wondering about all the hotel Checkin/out.
Hope this helps.
Enjoy planning your trip to Japan and congratulations to your upcoming wedding!