The final certificate (without poison and with SCT proof) is usually not published in any CT logs but you can submit it yourself if you wish.
Here's the pre-certificate for this web site's current certificate:
https://crt.sh/?id=23696530376
and here, just a few later in the log, is the finished certificate:
https://crt.sh/?id=23696528656
This is good practice, but it's also just easier, because if anything goes wrong, and sometimes things do go wrong, when the trust store says hey, please provide all certificates you issued with these properties, if you've logged them they are right there published in the logs for everybody to see - no bother, no risk - if you haven't then you need your own storage and better hope there aren't any mistakes. I'm sure LE do have their own copies if they needed them, but it sure is nice to know that's not what you're betting on.
† Poisoned pre-certificates are a "temporary" hack so that the certificate logging system can be demonstrated. If we ever really wanted this of course we'd develop a proper solution instead, right? Right? Every experienced software engineer knows that "temporary" usually means permanent in practice and so nobody was surprised by how this turned out.
Happy to see LE publish both, but others do not. Here is an example: https://crt.sh/?id=17293798014
Your won't find final certificate from digicert/globalsign in the CT logs.
Unless the owner publish it himself, API is opened for submission I think for everybody.
I'm not disputing that there could be a world where you're correct, but, it's not this world, which is why I even made that comment. That doesn't make relying on the logs for this a brilliant idea, it's just an observation that in fact it could work.
While they do not have direct SLAs, they still have to comply with rules enforced by browser vendors, as they will remove you from CT checks and you'll be marked retired/untrusted (you can find some in the above list).
This means a 99% uptime on a 90 day rolling average, a 1 minute update frequency for new entries (24 hours on an older RFC). No split views, strict append-only, sharding by year, etc.
I think OP's original idea would work.
The final certificate (without poison and with SCT proof) is usually not published in any CT logs but you can submit it yourself if you wish.
OP idea won't work unless OP will submit final certificate himself to CT logs.