Bloody Mary Poached Shrimp

1 32-oz bottle Bloody Mary mix, divided
1 ½ lb medium peeled, deveined raw shrimp, tails optional
4 cups ice
½ cup cocktail sauce
⅓ cup (2 ⅔ oz) vodka
⅓ cup olive oil
⅓ cup fresh lemon juice (from 2 lemons)
1 tbsp hot sauce (such as Tabasco)
1 tbsp Worcestershire sauce
1 tsp celery seeds
1 tsp black pepper
1 cup thinly sliced celery (from about 2 celery stalks)
1 cup thinly vertically sliced sweet onion (from 1 small onion)
Garnishes: celery leaves, lemon slices, lime slices, pickled okra, dilly beans, and/or pitted green olives

Place 1 cup water and 3 cups of the Bloody Mary mix in a large saucepan; bring to a boil over high. Remove from heat. Add shrimp; cover and let stand until shrimp are barely opaque in centers, about 8 minutes. Immediately stir ice into shrimp mixture to stop cooking; let stand until shrimp are cool, about 5 minutes. Drain shrimp and pat dry.
Stir together cocktail sauce, vodka oil, lemon juice, hot sauce, Worcestershire, celery seeds, pepper, adn remaining 1 cup Bloody Mary mix in a large bowl or a large heavy-duty ziplock plastic freezer bag.
Stir shrimp, sliced celery, and onion into cocktail sauce mixture. Cover (or seal bag) and place in the refrigerator to marinate for at least 8 hours or, preferably, up to 24 hours.
Transfer shrimp mixture to a large serving bowl. Top with desired garnishes, and serve immediately. (The dish can be made in advance. Store, covered, in the refrigerator for up to 3 days.)