Earlier quoted context omitted.
Transferring certificates from an untrustworthy CA makes no sense. Burn the certificates. Websites should just obtain brand new ones from a different CA. If you are running a website that's important to you, this should be at most a one hour operation (or, if politics and procedures delay you in obtaining a new cert, maybe you should have planned ahead and kept two different certificates on hand already)
By transferring I meant re-issuing automatically a new certificate, not keeping the signature. Of course this requires to re-authenticate the request. And that process has to be automated. A bit like the renewal of the certificate should also be automated.
I suppose you could downgrade on automatic transfer. I've heard people question the value of EV certs, and certainly a working DV cert is better than a revoked EV cert. Or you could insist every EV cert applicant verify their identity with two different CAs.