With an engine fire warning..... even one that came on for just a few seconds... I would have done the engine fire checklist or at a minimum had that engine throttled back to idle and turned back to base.
Consulting the company normally generates sub-optimum solutions! I once turned around on a US bound flight approaching Iceland having suffered a #4 hydraulic failure. With poor weather at destination the a/c would have requried a company expedition to an offline station to fix it. On return I was asked by operations 'Who authorised the diversion?' This is why airline managers hate pilots.