I rather stick to the simpler strategy of keeping the petrifying dog with me all the time and only switching when the dog on Jink gets petrification.
Remember that its not just a question of having the Petrifying dog paired with another dog. That would be too easy.
Rather we need to force the Petrifying dog to Overload before he turns us all to stone and we wipe. Now its true that if *any* dog Overloads it will reset the Petrification buff. But if any dog other than the Petrifying dog Overloads it will do ten times more damage to the raid. We can probably eat one of those and survive, but two mistakes like that and its Mass Rez Time =)
So we need the Petrifying dog to be grouped with the *right* dog! The right dog in this case being the dog with the *lowest* energy level of the remaining two (which except in the case of the first pull, will be the dog who last Overloaded).