Melt the butter in a skillet over medium high heat.
Add the shrimp and sausage to the skillet with half of the seasonings.
Saute until almost completely cooked through.
Stir in the garlic, and saute for 30 seconds.
Pour in the seafood stock, and add the rest of the seasonings.
Simmer the mixture for 5 minutes.
Slice the eggs in half lengthwise, and add the yolks to a mixing bowl.
Place the mayonnaise, mustard, relish, hot sauce and salt and pepper to taste to the mixing bowl with the egg yolks, and stir together with the tines of a fork until smooth and well combined.
Spoon a small amount of the seafood boil stock into each half of the eggs.
Pipe the filling into the egg whites.
Top each deviled egg with one shrimp and one slice of sausage.