Can you share both the action and the draft content? Without those anything we come up with is just a stab in the dark.
Again, this would come back to understanding what you have.
Searching for “copy to rich text” in the Action Directory doesn’t yield any results for me. Once we know what action it is you are referring to, perhaps you could explain your statement on styles a bit further?
Styles are usually managed through CSS and shouldn’t, generally at least, change the underlying HTML structure. At the same time, as has been indicated a few times above, HTML and ENML are not directly equivalent, so it may yet come back to the inherent constraints of trying to convert between the two.
The community in my experience is really helpful, but I think without the specific details, it’s hard to get a handle on whatever the one, or more, issues are that you are encountering. Which makes it more difficult an time consuming to identify an appropriate solution.