...there aren't any actual DBI objects floating around - DBI->connect is just a factory function for finding the right DBD driver, loading it, and instantiating it with the connection string.

That's not really how it works. You're right thatDBI->connect() is a factory method and that it passes much of the work over to the DBD but connect() also creates DBI driver and database handles which work in conjunction with the DBD's driver ::dr and ::db (and ::st classes for prepare). It's those clases of DBI that you need to override if you want to subclass DBI.