Why does salted cod turn chewy?
Assuming the cod was the same quality as before and you de-salted the fish in the fridge for 24 to 48 hours, then I would also guess overcooking.  Rendering the gelatin at 45&deg;C (as suggested in the paper @yossarian uncovered) should prevent the fish from cooking and give enough time to get it into the oil.  You can always cook the fish in a separate step after you made the pil pil.

Modern techniques for salting cod use less salt and create a product that will not be edible by future archeologists, so store in a dry cool place (tightly wrapped in the fridge).