Hi!
I probably wouldn't get a 14 day pass unless there is a lot of stuff you want to do not listed. The rail pass is best when spent on a lot of shinkansen and quite honestly the route I think is best won't have any shinkansen use.
I might get the Tokyo Wide Pass though only if your trips to Hitachi Seaside Park and Kawaguchiko were within 3 days, if not, I might not even get that pass. If within 3 days you could do the round trip to Hitachi and then the pass to go to Kawaguchiko. If you have a 3rd day you can use it to get as far as Kobuchizawa and would then pay out of pocket to get from there to Hirugami Onsen. There are a few different routes from there depending on time of day. From Hirugami you would then take a bus to Matsumoto. This is the part someone better at Japanese will have to give you estimates on since this is the only part I am a little unsure of.
From Matsumoto for 680 yen to 1440 yen depending on whether you use a local or a Limited Express to Shinano-Omachi and then you would start the Alpine Route
The Alpine Route costs what it costs I think close to 10,000 yen but is not covered by any of the passes you are looking at.
When you end in Toyama you would go by bus to Shirakawa Go or I guess if it is timed well, by train to Takayama, Actually, I would probably head to Takayama just pay attention to timing if you use the train because they don't run that often, The route is quite scenic though. It's ~3200 yen by Limited Express or 1700 yen by local. You will probably need to overnight in Toyama so you can catch the first train to Takayama
From Takayama you can do train or bus to Gero, I suspect the bus might be more frequent and is definitely cheaper. (~2000 yen by express and 990 by local The express only saves you 15 minutes, I suspect the one to take will mostly be based on when you want to leave. And the bus is about 1000 yen:
https://www.nouhibus.co.jp/route_bus/takayama-gero-line-en/#fare )
From Takayama take the bus to Shirakawa Go and then continue on to Kanazawa (
https://www.nouhibus.co.jp/highwaybus/kanazawa_en/#fare) Shirakawa Go is only accessible by bus, so even with a JR pass you would be paying for either a round trip or taking the bus to Kanazawa.
From Kanazawa to Kyoto is ~6900 yen by Limited Express and takes 2.5 hours. It's a nice train and runs about once an hour.
If you're just spending time in Kyoto until you leave Japan, you don't need a JR Pass since you are likely to be using private lines or buses or subways or walking.
I honestly just don't think you are spending the 47,250 yen to make it worthwhile.
I'm not a Shirakawa Go fan so to me, yes, you can 100% definitely do it in 1/2 a day. I think you could do it in even less, but again I am not a fan.
I wouldn't go from Hirugumi onsen to Gero. I'm pretty sure there is not transport unless you go back to Nagoya. I am pretty sure the routing I've just posted is the ideal routing though someone else might be able to tweak it even more so.
Good luck!
