Well, one route to consider is to join an industry group and ask around. In this case, you might try to identify the Buxiban Association that the major cram schools are in since you might want to join the group at some point anyway. As @Marco has already noted, Mandarin is going to be needed to be effective there
Maybe start with (ancient) threads like these and start googling names that you see for updated contact info
Another way might be via reaching the kind of companies that do business with the buxibans. They could tell if any of their clients are in trouble financially or who are looking to sell their business. For example, recruiting agents might notice a school has an unusually high teacher turnover rate.
Reach-to-Teach is an example of such an agent