Once you've actioned the recall items if the surge does not clear or an exceedance is still indicated the checklist advises you to shut the engine down. As you allude to this stage is not recall so in accordance with Boeing procedures you would wait until the aircraft was clean until you did so. However if you were to decide that the symptoms were now more appropriate to severe damage you could then action those recall actions which would secure the engine.
You have to make a judgement about how badly damaged your engine is and whether you can wait to shut it down. Personaly if the EGT stayed above limits after the initial actions I'd action the severe damage damage checklist. Better to be safe.