Solution? Simple:
No training crossings of LHR. Simple.
For those who believe otherwise, as an instructor, regardless of the quality of your pre-flight brief (and student!) you should be able to keep an aircraft on the required flight path. If not, you shouldn't be there!!! Are your studes' EOLs totally dependent on the brief?
It's about time some pilots stopped viewing crossing LHR as a jolly that they're entitled to. Perhaps it all comes from bored instructors wanting some variety .......