For what it's worth, I asked our Ops Specs folks about this. They spoke with their contacts at both Gander and Shanwick who advised they consider anything more than 2nm off the tracks a track deviation. They advised they expect one to call for such a weather deviation that would exceed 2nm off track. In the event one is unable to contact Oceanic, the table on the A/T chart applies.
Nobody is going to go through a CB in an effort to maintain track integrity. However, Gander/Shanwick expect that while deviating without a clearance (exercising Pilot-in-Command authority) one would continue to make an effort to contact Oceanic.