How do you change which content type a field is attached to (which one owns it?)
Well, this isn't the perfect solution, but may be a way to find it.

Change your content type to what you want to have it and export the feature. Them take a difftool (winmerge) and look at the diffrences between the old version of your features module and the new  one.

There's a good chance that you find out what to change.

Don't forget to take a DB Backup before you start.