[Josh Grisdale]

The Care Taxi Net (介護タクシー案内所) website has a database of accessible taxis around Japan. Here is their list for Nagoya City:

https://caretaxi-net.com/taxi/tokai/aichi/nagoya/

This one has an email address and is 24 hrs:

http://www.xn--n8jn2a84akb7bx3a.nagoya/contact.html

(The URL looks weird because it used Japanese characters)