Japan Rail Pass for Tokyo to Takayama

I will be traveling from Tokyo to Takayama and back in November. I'm having a hard time understanding the fares and seat fees. I will take the Shinkansen and the Hida Limited Express and would want reserved seats. Is there a price advantage for using a 7-day Japan Rail Pass or is it less expensive to simply buy the reserved seats?

Having a Japan Rail Pass allows you to make seat reservations for free, so take that into account when comparing. Usually the Pass will pay off only if you are making a long-distance return trip like Tokyo-Osaka. Tokyo-Takayama probably won't make a 7-day Pass pay off. Not having a JR Pass would allow you to ride the faster Nozomi Shinkansen (not able to be used with the Pass), so maybe buying separate tickets will be best.

If I take the Nozumi can I be certain of getting a seat without a reserved seat? That seems to save a significant amount of money. Or do the non-reserved cars tend to be filled in November?