Simple way to contact crew, as has happened in the past, is to get the affected company to ACARS message or Telcom the pilots that agencies are trying to radio contact them. Either company aircraft in the area can alert their company that the offending aircraft is not responding to ATC, or the controlling agencies can landline call the company operations about the situation.
A similar event occurred with an EK crew who were given Final Warning letters and a financial penalty.
Most modern FMS/C's allow time markers or a fix range or radial circle to be put at any waypoint. Be professional and alert yourself at the FIR waypoint as well as good RT comms discipline by ALL in the air (listen out and no chatter on 121.5) and on the ground (handover before aircraft is out of reception range).