Well you've already talked about a couple of the big things... Check their headjoint corks to see if they're loose. They wear out every couple of years in my experience, and sometimes you'll have this airy problem and discover it basically falls out if you turn it slightly. It should seal completely. Could also be trill keys not sealing too.

Otherwise if that's in place you can try going back to the headjoint if they're younger players. There's a tool called a Pneumo Pro that can help with kids understanding where to visualize the air.

To add to the harmonics it sounds like you're already exploring, Kathi Blocki released a really cool packet of Jingle Bells with changing fingerings with the harmonics to keep getting Jingle Bells out. (I was totally geeking out over it when I bought it) I would consider that an 8th-12th grade tool. (Younger if they study privately, which I'm guessing these don't)

If none of those solutions work see about getting a clinician in, or zooming with someone. There are a lot of other things it could be. This year with COVID it's not making it easy to explore all of the problems we're seeing with embouchures!