Is there a way to tell which campaign missions I've already won?
Unfortunately, the game doesn't keep track of this. According to the XboxAchievements.com Achievement Guide:
The game does not keep track of which maps you've won on, so make sure you copy this list and mark them off as you go or use the Excel file linked in the Road Map.
The first post in that thread links to a spreadsheet that you can download to keep track of which campaign missions you have won, as well as which maps and modes you have played on for the "I've Seen It All" achievement.