1. Ask for a list of all issued certificates, get signed certificate timestamps (SCTs) for all of them, and require that all certs issued by the CA have working CT. This essentially prevents all further misissuance (or, at least, makes it very public).
2. If the CA is so bad at life that it doesn't know what certificates have been issued, require CT for all new certificates (trusting the self-stated signature date on the certificate), and have a sword hanging over their head if any evidence arises that the CA has backdated any certificates.
Chrome did #2 for Symantec, and then (I believe) moved to #1, and Symantec is definitely a too-big-to-fail CA.
https://security.googleblog.com/2015/10/sustaining-digital-c...
https://knowledge.symantec.com/support/ssl-certificates-supp...
https://groups.google.com/a/chromium.org/d/msg/ct-policy/hNK...
Of course, Mozilla needs to add support for CT for this approach to work.