I think... a lot depends on what you want to do and what your interests and priorities are...
If you already spent most of a day visiting Shirakawa Go and staying there overnight, then yes, if you got to Takayama by 10:00 I could easily see you seeing the town and being ready to go by 14:00 or earlier. Though you might not make it to Matsumoto in time to see anything that day, you would still have time to see things there the next morning before heading to Kiso.
But a lot depends on your touring speed and what interests you. I did a day trip to Shirakawa Go and that was more than enough time for me. But some people really love it. For a lot of people staying overnight is the highlight of their trip. Given my choice I would prefer to stay in Matsumoto or Takayama. I do prefer cities though, which I know makes me an outlier on this forum. I like some countryside but I am not bothered by spending a lot of time in cities. I also use to live in the countryside and I suspect most people posting on this forum live in cities so the countryside is a lot more exciting. If you decide you want to skip Matsumoto, again there is a bus direct to Kiso from Takayama. It's long, but I think that is the only time it is longer by public transit than driving.
If you do decide to go Kanazawa to Shirakawa Go to Takayama to Matsumoto while in Tokyo you should buy this ticket:https://www.nouhibus.co.jp/english/ticket/
Supposedly it is only available via JR East. There is a slightly more expensive one via bus for 6000 yen but why pay 500 yen more because you didn't get one in Tokyo.
Ah, actually I was wrong, the bus from Takayama directly to Kiso probably makes the most sense unless you want to go to Matsumoto. The bus only takes just under 3 hours from Takayama to the Kiso Valley:https://www.nouhibus.co.jp/route_bus/magome_tsumago_line_en/
Though you would need to overnight in Takayama to catch it since I don't think you can get from Shirakawa Go to Takayama in time. If you are on a budget, going by bus from Kanazawa to Shirakawa Go, Shirakawa Go to Takayama and then Takayama to Kiso is hands down the cheapest and fastest and should be under 10,000 yen per person. You would then just need to pay to get from the Kiso Valley to Nagoya and Kyoto. If your trips Tokyo to Kanazawa, Kiso Valley to Nagoya, Nagoya to Kyoto, Kyoto back to Tokyo all fit within 7 days a JR Pass might make sense and pay off, if all those trips do not fit within a week it is likely a JR Pass does not pay off. If you have a good idea of when you are traveling in advance you can save some money buying a ticket ahead of time. There are pluses to not having a JR Pass. The Nozomi are much more frequent and are faster. There are of course buses and other routes between locations, but it really depends again on money vs. time spent. In the case of the bus between Kanazawa to Kiso, using JR trains saves you no time and Shirakawa Go is only accessible via bus. I think you only save 1 hour by rental car and it costs considerably more. However, if you opt for bus from Kyoto to Tokyo, it will take ~7 hours. To me 3 hours vs. 7 hours is a big difference but it might not be to you.
I hope this helps!