I have had to descend in MNPS airspace three times, once for a pressure door unlocked and twice due to engine shutdowns (aint't the military a wonderful training ground) and it was usually a non-event. Declare the Mayday, or otherwise, tell the radio operator (Gander or Shanwick) you have a problem and within a moment you will be speaking directly to an OAC controller who can make a traffic decision quickly. Once, it was "descend on track, at FL 280 or below proceed direct Gander, advise when level and direct CYQX." Another time, pressure door unsafe, it was "descend on track to FL100 and advise when able higher level." We could not then get above FL 290. The last time, the OAC was unable a clearance immediately, we offset, 30 nm at the time, and descended. Once level, with OEI, recleared onto the track coordinates to the landfall fix at the driftdown level.
Just take the time to get your drills done, advise the OAC what you need and it shouldn't be a problem. Now I operate on random routes above the track system, I think it is harder-the first imperative is to change the flight plan to the nearest track AND establish an offset prior to descending. A whole bunch more keystrokes. And I have had routes that cross three tracks, so at each significant fix, you have to have yet another track in mind for emergencies.
GF