I think this whole CA system is needlessly complex. Your registrar should be providing you with a free certificate for your domain and that should be the end of the hassle.
Every CA that issues DV certs for public DNS names takes registrars' databases as the ultimate ground truth about domain ownership -- at least for the domains that the CA is willing to issue for -- so the DV-cert-issuing world is reliant on them to be correct, secure, up-to-date, and so on. That's true whether the CA is using whois data plus DNS data, or just DNS data, to verify domain control.
(In saying that, I thought about the idea that Let's Encrypt may use safeguards to limit issuance based on historical observations of domain control and prior issuance history by other CAs. For example, our draft ACME spec has a mechanism where we could ask a requestor to prove control of an existing subject key from a cert that we know was issued for the same subject domain by another CA. So if we've already seen a valid cert in the wild, or in Certificate Transparency, for example.com, we could say that you have to show that you have control of the key in that cert before you can get a new cert from Let's Encrypt for example.com. But all of those things ultimately go back to what registrars said in the past, even if some of them are independent of what registrars say today.)
https://en.wikipedia.org/wiki/DNS-based_Authentication_of_Na...
You can publish and sign your TLSA records today, without interfering with your current CA signed certificates.