Since I don't want to redo the timings and edits of my existing project, but I want to upgrade to a better movie maker for more options (including editing existing parts, so I cannot simply render this first...), is there a good way to do this?
To be honest I don't think this would be possible. Your best bet would probably be to export the video and import it into Vegas. Just make sure you keep a record of the timings. Sony Vegas and Windows Movie Maker are two very different programs with very different editing tools. Unless there is a converter somewhere that I have not seen then I would just export as a video file.