I'm not sure that would work as a GSoC project because just re-implementing the text editor would be quite a lot of work. I think it would need to have both Rich Text and Markdown editor, which of course is even trickier. The editing experience is also likely to be inconsistent - for example how about vim support, themes, etc? Users could reasonably expect this to work.
What would be your plan for all this? Also would you support resources and Markdown plugins?