Well, a double loop failure is not considered a LAND ASAP situation by Airbus. Other than that, I'm not sure that us mere pilots can come up with a watertight risk analysis for this scenario. What do we know about engine fires other than how to extinguish them? What do we know about other indications of an engine fire? Would EGT rise? I guess it depends. Would oil pressure drop? I guess it depends. Would the engine show any other signs of fire until it's way too late? Who knows!
So other than closely monitoring the engine, shutting it down at the first hint of trouble and firing both bottles I'd continue to destination. That is, if there is any maintenance available at destination! If the instructor is not happy with that answer, then ask him why the MEL does not prescribe any additional procedures.