Your story is similar here
http://www.japan-guide.com/forum/quereadisplay.html?0+68003. Perhaps, I will be repeating or pattern my answer on what I deem easier. Caveat of the wordings and complications. When it comes to travelling in Japan,
everything should be made as simple as possible, but no simpler. - Albert Einstein If you have already searched for the answer hence your confusion then I will keep on repeating what I deem possible in my humblest opinion.
I suppose to travel later this year the same way, on night time, in this manner - train ride all the way from Centrair to Shin-Unuma Station via Meitetsu then transfer to Unuma Station via JR local line that will arrive in Takayama at 12:07 AM! However, I have to forego that plan for the fact that my airline arrival is unreliable and that I have different itinerary already.It was discussed here many threads ago that there used to have Centrair to Takayama bus operation but was already discontinued.
There are bus operations going Takayama in Nagoya and Gifu. There is also the train ride. I will concentrate my answer pointing from Nagoya as I move forward.
Details of Chubu Airport or Centrair transfer guide can be found here
http://jprail.com/sample-itineraries/airport-access/chubu-ngo/chubu-na....
You can connect by bus from Centrair to Nagoya. If arriving at 840, the first bus to leave for Nagoya will be at 915. See schedule here
http://www.meitetsu-bus.co.jp/english/area/centrair.html. Airport bus access at Centrair is here
http://www.centrair.jp/en/to_and_from/access/bus.html. With bus ride, it will take you directly to Meitetsu Bus Center from Centrair.
If 915 seems too tight, you can take Meitetsu train. Check schedule here
http://www.meitetsu.co.jp/eng/timetable/centrair/timetable/access_e05_.... Price is JPY 870 for limited express or semi-express then add JPY 230 on top of normal ticket price if taking ƒÊSky. Since you will arrive at 840, then you can take any train between 9 to 930. Train ticket can be purchased at the Centrair.
Meitetsu Nagoya train station map is here
http://www.meitetsu.co.jp/eng/route/major/nagoya.html.
From Nagoya going to Takayama, you can either take the bus or train.
Bus operators from Nagoya to Takayama are Nohi Bus and Meitetsu Bus. Schedules are shown here
https://www.nouhibus.co.jp/english/highwaybus/nagoya.pdf and
http://www.meitetsu-bus.co.jp/english/area/takayama.html. Ticket price is JPY 2,980 one way.
If you take the bus from Centrair to Meitetsu Bus Center, you may ask how to go to bus terminal 7 on the 3rd floor there going to Takayama.
I am not sure if you will arrive at 4th floor or 3rd floor in Meitetsu Bus Center. If 3rd floor then you are in a major luck! If anywhere else then ask the driver. If by train, then walk your way from Meitetsu Nagoya to Meitetsu Bus Center. Access is found here
http://www.meitetsu-bus.co.jp/english/reserved/access.html. You may follow the written guide. You may have to review as well the Meitetsu Nagoya train station map to connect the puzzle.
Bus reservations can be done at the ticket window of Meitetsu Bus Center or book online via
http://www01.jrtbinm.co.jp/en/takayama/index.html.
If you are riding the bus or train from Centrair to Nagoya, give yourself 3 to 4 hours window (exaggerated) including immigration check, for transferring and to subject yourself in the bus availability going to Takayama.
Train ride from Nagoya until Takayama is another story.
If you do not want train transfers from Nagoya going to Takayama, Wide View Hida limited express is the train ride. However, that limited express is operated by JR which is another (or biggest) train operator. That means you will have to transfer stations when you get to Nagoya on street level! Transfer guide between Meitetsu Nagoya and JR Nagoya stations had been discussed here
http://www.japan-guide.com/forum/quereadisplay.html?0+115000. Just follow that thread.
You may check the Wide View Hida schedule on Hyperdia or here
http://touristpass.jp/en/takayama_hokuriku/images/modal03_tt.png. Unreserved seat costs JPY 5,510. Reserved seat is JPY 5,830.
I hope this will help. Whatever you deem untaxing, it will be your call.
