@nagaemas - this works great!
it perfectly saves the html editor's content to the textarea of the text/html tab itself.
BUT there's still one tiny problem: Say you're editing in text mode with the text tab active. WordPress remembers that. So the next time you edit a post or page it initialy has the text tab active - and then there's no active editor set etc. the instance can't be found and handled UNTIL you have clicked the Visual tab.
So i'm almost there but now i'm trying to find a solution for that last small issue.
I'll post it when i find something!
Thanks to your question I also discovered this!
If you look at wp-admin/js/editor.js and the go function you'll see that the editor is instantiated if the user selects the Visual tab. Maybe initializing the tinymce yourself might be a solution, but that seems to be bad practice
I am currently also looking for the solution, let me know if you found it