If you fly from Tokyo to Itami, you could do a JR Hiroshima Pass (which would allow Nozomi which REALLY helps when visiting Hiroshima, when I went to Miyajima in June 2017, there was no availability for reserved seats from Hiroshima to Shin-Osaka until after 19:00, and yes I tried to book 4 or 5 days ahead of time. We happened to take an early Hikari from Kyoto to Hiroshima at 8:00 am.) If you've not bought your airfare yet just look into an open jaw arrive in Kansai depart from Tokyo. My closest major airport doesn't have a direct flight to Kansai, but the price to fly JFK to Itami, Tokyo to JFK was the same as a round trip to Tokyo.
With the JR Hiroshima Pass you can get as far as Tsuruga going to Kanazawa and would then just need to pay an additional 4620 yen when you get to Kanazwa. The trip by limited express takes about 2 hours from Kyoto Station. Or you should be able to do a combo of the JR Hiroshima Pass for 15,000 yen and JR Hokuriku Pass for 5000 yen. (for a total of 20000 yen.) And would get you to Hiroshima, as well as to Kanazawa and to Toyama to do the Alpine route.
So for your itinerary I would:
Keep Day 1 as in just fly vs. the train
Day 2 Still travel around Kyoto
Day 3 Make this your Yoshino day since I don't think a Kintetsu Day Pass Pays off, but you can see if it does
Day 4 Start your Hiroshima Pass and use it to just go Osaka (day 4+5 can be swapped easily)
Day 5 Visit Hiroshima
Day 6 visit Arashiyama and then go to Kanazawa using a combo of the two passes (since you will be in non-reserved seats it should work fine and it means you're traveling ~1.5-2 hours less this day)
Day 7 Depending on what you want to do in Kanazawa do Kanazawa.
Day 8 Alpine Route (you can either overnight in Murodo or even do the complete route and end in Matsumoto)
Day 9 Matsumoto
Day 10 Bus to Takayama (if you're traveling light or there are lockers you can even stop off in Kamikochi or go to Shin Hokata this day)
Day 11 Takayama
Day 12 Takayama
Day 13 bus back to Matsumoto go to Yudanaka
Day 14 Snow monkeys and then return to Tokyo
Day 15 Tokyo stuff
Day 16 Tokyo stuff
Day 17 Tokyo stuff
Day 18 leave and Tokyo stuff
It's possible a JR Nagano-Niigata train pass will pay off, you'd need to do the math, but I suspect not, it's only 8200 yen from Nagano to Tokyo with reserved seat and 2320 yen for a non-reserved seat on the Limited Express between Nagano and Matsumoto. I took this train several times last June and it was just not that full. though a reserved seat will only set you back 2840 yen The Hiroshima Pass and Hokuriku Pass *WILL* pay off since Kyoto or Osaka to Hiroshima round trip is more than 13,000 yen and it's close to 5000 yen just from Tsuruga to Kanazawa, and the pass will also cover the shinkansen to Toyama. You could get this pass: https://www.alpico.co.jp/en/special/
which would cover all the bus travel you want to do around the Alps. You could possible do the Alpine Route back to Nagano and do Yudanaka before going to Matsumoto. Even with a JR Pass, you'd be paying out of pocket for transport to Shirakawa Go, Shin-Hotaka, and actually doing the ropeway. But make sure the pass pays off, there are a lot of different bus specials for the alps region. Personally, I would pick more time in Okuhida or Kamikochi over Shirakawa Go. I loved the Hida Folk Village, I thought it was incredibly well presented and super interesting and my child loved it too. I went to Shirakawa Go in 2010 and it just felt like a huge tourist trap, it's not somewhere I've had an interest in returning.
In that case it would be:
Day 8 either overnight in Murodo or continue to Nagano
Day 9 continue Alpine route and end in Nagano or visit Nagano or see the monkeys
Day 10 Matsumoto (you could do days 10-13 with the 4 day Alpine Pass. I would just make sure you are starting off nice and early from Matsumoto and return as late as possible on the 13th.
If you move it around like that you will be going back to Tokyo from Matsumoto, which is 6500 yen with a reserved seat.
Sometimes getting non-nationwide passes might not necessarily even save you money but can save you time. I've been going back and forth on my next trip whether to get a nationwaide pass or pay out of pocket for the shinkansen from Nagoya to Tokyo and do a JR East Pass. I've decided to go with the latter, because then I don't need to overnight in Nagoya for the 7 days work and can immediately head to Tokyo from Nagoya. This gives me a full extra day in Tokyo, which makes my schedule easier.