rescue Inno tables from an abandoned data directory?

I abandoned a MySQL 5.22 database that quite suddenly andthat I wasn’t able to start up again. The data directory consists of a mix of ISAM and Inno tables.  I  was able to copy the ISAM tables into a new 5.6 version, and they work.

I understand that INNO tables are different because different tables share a common table space. The MySQL documentation refers to a “cold backup,” where you copy the separate files after a “slow shutdown.”  It doesn’t tell you what to do with them after you’ve put them in a “safe place.”

In my case, I can reproduce Time machine backups of data directories at varying times. At one point I was able to replace the non-working installation with an earlier installation, but then it failed unpredictably.

Are the Inno tables on Time Machine useless, or can I rescue data from them?

I’ll be grateful for help