Your first recipe has too little soy sauce and sugar, and too much sake. Here's my basic sauce recipe (FYI, it's called kabayaki):
1/2 cup Soy Sauce
1/2 cup Mirin
1/4 cup Sugar
1/4 cup Sake
1 piece Fresh Ginger, about 1", peeled and thinly sliced
Cornstarch slurry (optional)
Combine all the ingredients except for the slurry in a saucepan. Bring to a light boil then simmer for 10 minutes. Add a little slurry if you want the sauce thicker. Remove from heat, strain, and let cool to room temp.
"Boldness has genius, power, and magic in it."
Johann Wolfgang Von Goethe