To add a bit to what @LikeBike said, because it's getting late for me.... If you're in the Magome and Tsumago area it's going to run you 4-5 hours I believe to reach Takayama. You need to get back to JR and then take the train to Matsumoto and then transfer to a bus there. If you're interested in Hirayu onsen or the Okuhida area in general, it might make sense to visit on the way from Matsumoto since Hirayu onsen should be a stop on the bus route.
I was looking into some hikes in Nikko at one point. I think one of the lodgings I was looking at, The Nikko Teddy Bear house, offered some interesting lead hikes. We've decided to skip Nikko this trip, but it is something to look at. If you're there when it's koyo time around Lake Chuzenji and the Irohazaka Route, it will be quite pretty but also possibly quite crowded.
Takayama to Kanazawa can also take a couple of hours. You either need to take the Limited Express to Toyama and transfer there to the shinkansen or take a direct bus. The train can be faster you just need to make sure you make one of the 4 or so Hidas that do that route.
I like Nara, and I could totally see why someone would want to spend the night there and I think a few people on this forum like overnight in Nara more than Kyoto.. However.. if you're overnighting in Nara in hopes of speeding up your trip to Koya-san, it's not going to happen. The fastest way from Nara to Koya-san involves back tracking almost into Osaka to catch a limited express private line Nankai train. You can get from JR Nara to JR Hashimoto Station (to transfer to the Nankai line) but the route is circuitous and slow. It's mostly local trains with odd schedules and it will take you longer. There are some interesting walks. It's more than 1 day but... https://www.japan-guide.com/ad/yamanobenomichi/
I'm planning to do part of this route over the Summer.
Also, you're really not spending a lot of time in Kyoto. You have 1 full day and part of 1 day, but depending on when you reach Kanazawa the day before and what you want to do there, you might have limited time in Kyoto that partial day.
Nikko has some high end ryokan with onsen or there is always the nearby Kinugawa onsen. I know there are onsen ryokan in the Tsumago and Magome area and i've stayed 2x at the Takayama Associa Hotel which has two floors of onsen. There are also onsen ryokan in Hirayu (I've only day tripped there but the onsen were lovely) as well as in the Okuhida region.
I agree with @LikeBike about seeing about an open jaw ticket. I don't have a direct flight to KIX from my home airport, but it actually cost less to fly: my airport to Tokyo to Itami then Tokyo to my airport than it would have cost for a round trip from my airport to Tokyo.
I looked into renting a car in Takayama and dropping it off in Matsumoto 2 years ago. The drop-off fees were around 10,000 yen.