Logic redrawing overview files every time

This could possibly be a permissions issue. I seem to recall a similar issue on the Logic Pro forum where someone commented that if he set permissions so that "everyone" could read & write (e.g. your students) it doesn't let the overviews be written permanently. If this is indeed the case, you might need to reset permissions so that you are the only one who can save the project files.

Of course, you could also try trashing the logic .plist file in your user library preferences folder. Logic will simply create a new one the next time you launch it. You may want to keep a copy of your current one as a precaution if you've set LE up in a particular way for your class.

Also, if these are all brand-new iMacs they are probably running Mavericks, which has proven to be problematic with regards to Logic 9.

Another thing to consider: someone experiencing a similar issue read that long file names could cause this and once he shortened his file names the overviews stopped refreshing every time the project was opened.

Also, if it turns out that you are indeed running Mavericks you might consider installing the latest GarageBand on your computers. It's free and is for all intents and purposes the new "Logic Express X" since the interface and application core are like Logic Pro X. And GB now comes with Drummer, which is very cool. You could even use it just to create drum tracks which you would then export as audio or MIDI files and bring into LE9.