^ This basically is what I thought before I scrolled down to see it already suggested.
But then maybe there's a reason why you don't want to use a whiteboard system. In which case, I'd just go with a shared Outlook calendar. On each day, have four 8:00 to 8:30 meetings, one for each team. In each meeting you set the meeting title as Team 1, Team 2 etc. Then in the body text of the meeting you Type in which Crew is in that team. You can also add in any notes and comments relating to the tasks you need them to achieve etc. Use colour categorisation for the meetings to enable quick identification.
The downside to this is that it is slightly more labourious than a drag and drop method. However, it is easy and anyone can do it so requires little training and anyone else can take over when you're off work with the shits or lounging on a sunny beach with the little shits. Also has the benefit of using a piece of software that you're already using which is usually very stable.