>> How do I recover them, and do you think this is wise? At this point, I
>> still think it might be a better idea to do a complete reinstall /
>> restore / transaction log run.
There's no need to reinstall :-) It's not MS Windows, it's just InnoDB.
As others have said, I'd try to do a global LOCK TABLES (I wouldn't do
a FLUSH TABLES because I'm not sure how missing files might be handled
-- it could crash) and a full dump. Then just shut down MySQL and
delete *all* the InnoDB files and let it initialize with fresh files on
restart, and import. You should be fine. But I'd do it ASAP because in
the meantime you could have a crash.