Fill a large pot with 1 quart water. Cut 4 limes in half, and squeeze their juice into pot; add lime halves. Bring to a boil, then turn off heat; let mixture steep about 10 minutes. Return to a boil.
Add shrimp to pot. As soon as water returns to a rolling boil, pour shrimp mixture into a colander; discard cooking liquid and limes. Return shrimp to pot; cover, and let stand 15 minutes. Transfer shrimp to a baking sheet and spread them out; let stand until cool enough to handle.
Peel and devein shrimp, and cut into thirds. Transfer to a medium bowl; stir in 1/4 cup lime juice and the scallions, chiles, vinegar, thyme, and oregano. Let stand at room temperature 1 hour, stirring occasionally.
When ready to serve, stir avocados, cilantro, and salt into shrimp mixture. Serve with tortilla chips.