Well, it's almost never actually LE misbehaving if it's just n=1 
But we simply don't know, currently, what's really underneath that "Certificate already generated" output, even though we don't see that certificate in transparancy log aggregators such as crt.sh. It might be anything underneath 
In the mean time the Let's Debug tool gives your site also the "everything should be good to go" result (Let's Debug).
While I also think your steps 1 and 2 are a good thing to try first, maybe you should look at CertSage as an alternative to shell access and Certbot. CertSage doesn't require shell access and is fairly easy to use. And comes with cPanel integration for installing the certificate semi-automatically, although I'm not sure that also works with TSO Host.