well, you are right, shin hotaka has many options so sadly i have not been in all ryokans to tell you about all of them
i can just tell you of the very beautiful rotemburos i have seen:
* 新穂高の湯 is nicely framed by rocks almost in the riverhttps://www.google.com/maps/place/
* you can go up the ropeway: Shinhotaka Ropeway (i didnt found it so special, since i am from a country with many mountains and ropeways, also i am generally in this area during summer or winter, so i never saw the real koyou, but you seem to be there in the right time, so might give it a try)
* 白出大滝 is secret, super nice, but you need good mountain equipment and i think it is probably a little bit too hard for just casual touristhttps://www.google.com/maps/place/
* but: drive to sanbon taki: it is a super easy walk and extremly beautifulhttps://www.google.com/maps/place/Sanbondaki+Fallsemail@example.com,137.582...
** you can also combine sanbontaki this on the same day with shirahone onsen, Awanoyu, a very famous onsen for blue water where it is even mixed (dont worry, due to the blue color of the water noone is going to see you naked)https://www.google.com/maps/place/Awanoyufirstname.lastname@example.org,137.6244923,319m...
*** after you saw Awanoyu, you can go also to the next door facility かつらの湯丸永旅館 which is not so famous as Awanoyu, but therefore more quiet
* Hirayu Onsen with its Hirayunomori is also nice. it is also a good place to stay from value / money https://www.google.com/maps/place/Hirayunomoriemail@example.com,137.551547,...
* when you are in this area, try Hida beef, it is considered one of the best of Japan (take care, it's expensive!)