I'm not an authority but I hope this helps. Adapted from a book on all types of cured meats and sausage.
One thing to think about is the book uses instacure #1/pink salt in the brine while curing. The reason is the threat of botulism. I am not sure if this is a point you brined or one done commercially. Or how 6-8 hours of cold smoke will affect it.
This is the suggested method adapted from the book is. Preheated smokehouse @ 130* for 1 hr with dampers fully open. Close dampers to 1/4 open and apply light smoke for 2 hours. [Then raise the smokehouse temp to 220* until the meat has an internal temp of 175*] Instead of raising the smokehouse temp you would throw it on the egg until it is done to your preference. I have heard everything from 160* to 180* on the final internal temp.