Heat the olive oil in a skillet over medium-high heat until it shimmers. Saute as many shrimp as you can fit in one layer, until they're browned at the high spots. Repeat the process till all the shrimp are cooked. Set the shrimp aside to cool.
In a shallow bowl big enough to fit all the shrimp, combine the Creole seasoning, lime juice, syrup, vinegar, cilantro, Worcestershire, salt, pepper, and Tabasco garlic pepper sauce. Mix well, then add the shrimp. Cover and marinate, refrigerated, for six hours. Once or twice, stir the mixture up again.
Right before serving, slice the avocados and place them on plates. Spoon the shrimp atop the avocados, and top with the shallots and jalapenos.