What is a good substitute for puffin?
I have had smoked puffin once in Iceland. It made me think of a lean, strongly-gamey/livery duck/goose breast that's been sous-vided till very tender - I remembered the grains (meat fibres) to be very fine. There was a mild sort of silky fishiness (that was masked by the smoked preparation) too, but I'm not sure if I imagined that knowing the puffin was a seabird. 

I googled faroese puffin (here), and I think the 90min cooking time is meant to ensure that the batter sewn up in the bird is properly cooked -> making the puffin merely a slow-cooking vessel for the cake within. 

If I had to hazard a guess, and you could forgo the aesthetic of a whole stuffed bird, then perhaps you could mimic the flavor by sousviding goose/duck breast that had been sewn up with the batter, with a bit of liver in the bag (unless your duck was already very gamey). I'm not sure how (or why) you would add that element of fishiness.