Typically we have 1200 to 1800 long clips capped in our media bins during a broadcast edit. As we get done with the first rough cut there are only say, 600-700 "shots" used in a timeline. Is there a way at that point to save a version of the Vegas project file with only the shots from the timeline saved?

Click on the lightning bolt in the Project Media tab. That will remove all unused clips from the Project Media. Now do a File - Save As and give it a new name.