Chubu Centrair to Nagoya Station中部国際空港 → 名古屋
The Meitetsu μSKY (ミュースカイ) takes about 28–30 minutes to Meitetsu Nagoya Station and costs ¥1,430: a ¥980 fare plus a ¥450 μ-Ticket, because every seat is reserved. Buy at the airport station or on Meitetsu's website. The ordinary express takes about 48 minutes for ¥980 with no seat ticket.
Meitetsu Nagoya is a short walk from JR Nagoya, where the Hida and Shirasagi leave: allow 15 minutes for the walk and the JR ticket gates, 20 with luggage. If you land after about 18:00, sleep in Nagoya and start fresh: the last Hida to Takayama leaves at 20:17, the last Shirasagi at 19:48. Stays near the station.
Send the big suitcase ahead. The forwarding counters in the terminal (takkyubin) usually deliver to a hotel in Takayama or Kanazawa the next day, so you ride with a day bag.