It is kind of odd to characterize Takayama as offering ga more authentich experience than Kyoto. If you are wanting traditional Japanese culture and history, Takayama canft even begin to compare to Kyoto. You just have to make an effort to minimize the negative effects of overtourism that are starting to give Kyoto a bad reputation, and you need to be very clear on what you mean by gauthentic.h But in a sense itfs a lot easier to hop on a train to Takayama than to do the careful and thoughtful research needed to experience the classic (historic/traditional) essence of Kyoto. And you indicated right up front that you donft mind 8-hours of train riding in a day. The nice thing is, at least half of that is quite scenic and enjoyable. So is Takayama gworth ith ? Well, most people like Takayama a lot. There are no ggrass hutsh there but I suppose you mean the traditional farm houses (ggassho zukurih style). So if what you really want is to go to Takayama, then why not go there, assuming you can get the train reservations? You certainly donft have to go to Shirakawago to see traditional farm houses, and you absolutely donft have to spend the night in one. They can be drafty, smoky, and noisy, and usually have shared toilet and bath facilities. (There is no question that those qualities are authentic, though.)
If you just want to see grass huts, note that Miyama is a lot closer to Kyoto, and apparently has a lot of them (although they are a different style from the ones in Hida). https://www.japan-guide.com/e/e3985.html
But it doesnft have some of the other attractions of Takayama, including the fairly nice and extensive town preservation districts. Takayama is way better for shopping, too, although it gets insanely crowded at times.
One observation about your itinerary is that is based on extremely popular tourist attractions. Visiting such places can sometimes be at odds with having an gauthentich experience of Japan, you know. If you want to experience the real Japan, then you have to be willing to ditch the top-ten lists, and you have to get realistic about what grealh means. Heavily overtouristed places by definition are no longer grealh in the historic or traditional sense!
If you want to go to Miyajima and see the famous torii, be sure to check progress on the renovations that are going on there. It could be a bummer to get there and find it covered up.
Beppu/Yufuin is pretty far afield from Kyoto, although at least you have an overnight there. If it were me, I would probably pick some place closer to Kansai. There are literally hundreds of possibilities. And be aware that some people absolutely hate Beppu, while some people find Yufuin to be gdisappointing.h So whether that trip is gworth ith might be a better question than whether Takayama is, probably. Think about the experience you want to have, and then do some more research.
In general, Ifd say that if you really enjoy train riding (and donft mind long days), then your itinerary isnft all that bad. Most people simply cannot relate to that much train riding in such a short period, but if you know that it will be fine for you personally, then donft listen to the many shrieks you will get about it.