I suggest, that the "virtual row" (the last row of each document, where a new content item can be entered) already "knows" in which project and document it will be created (before really creating the item).
This would give the possibility to e.g. have contraints on the category per project. Today the full category list of the content type is shown. When I constrain the category by project (or document ID) it does not affect the virtual row, because since it is not created yet, it does not "know" in which project it will be created. But since the project can not be chosen by user, it would be possible to hand over such information already to the virtual row.