Step 4: Peel tongue
Next I removed the tongue and peeled off the skin. Since this is the discolored yucky-looking bit, things started looking up after its removal.
The tongue itself is a big chunk of almost solid mustle, with a bit of connective tissue in the middle that requires prolonged heat to melt. Without the skin it looks far more like a more traditional meat, albeit in a strange shape.
The skin came off quite neatly; I only had to use a knife to coax some thin bits underneath to come off without tearing too much. There are some ancillary bits (blood vessles, fatty glandular bits, etc) attached to the lower sides of the tongue's base that can easily be removed at this point; they'll feel different, squishy and decidedly non-meaty, and thus can be easily separated from the good parts.
The Joy talked about removing roots, small bones, and gristle; I found none of these things. Perhaps a differently-cut tongue would have small bones attached? They didn't give any pictures or diagrams.