I mention CAA DNS records in the end of the post, but unfortunately the last time I checked my registrar did not offer the possibility of creating these records... :(
Oh Dear! looks really interesting (though I won't pay for monitoring my personal blog).
I am not sure I fully understand your HTTP-only remark, since how the communication is made (HTTP-only, HTTPS, IMAP, etc.) is not related on how the certificate is generated (which implies CT).