I removed cancel, reordered, redesigned and labeled the remaining two options to:

In addition, the previous update did keep the established "Publish Live" checkbox but it appears after the initial publication of the content.
It also introduced a new dialog if a member decides to draft a live submission:

Thanks for the feedback on the button options themselves, I like that it lead to only two options and it is clearer now what both do.
What do you think?
Preview button does not make it clear that the submission is saved.
Anyone who has been on PMC knows the old "publish live" checkbox and can guess that the preview button does exactly that. However, right now the publish process can be very confusing for new users.