I have a feeling it stated in the old CAP53 that the QXC had to be a flight totalling 150nm landing at least two intermediate airfields.
That was certainly how it was worded for the 300nm XC trip for the CPL. Had to look into it then as we ended up making it to a third airfield for some fuel!
I haven't had chance to go through LASORS but personally would say the student would have to go through the trip again.