Cook rice according to package directions. In large bowl, stir together vinegar, salt and sugar until dissolved. Mix in rice. Let cool completely. Refrigerate, uncovered, for about 1 hour or until well chilled.
In glass bowl, combine shrimp and 1/2 cup lime juice (add more lime juice, if needed, to cover the shrimp and allow it to float freely to ensure that shrimp “cooks” evenly throughout). Cover and refrigerate for about 3 hours or until shrimp is opaque through to center and slightly firm. Drain well.
In separate large bowl, stir together tomato, cucumber, radish slices, red onion, serrano, cilantro, basil, lime zest, salt and remaining lime juice. Add shrimp; toss until well combined.
Shape 2 tbsp rice into ball, then flatten into round. Repeat with remaining rice. Heat vegetable oil in large nonstick skillet set over medium-high heat. In batches, cook rice rounds for about 5 minutes per side or until golden brown and crispy, adding more oil as needed. Transfer to paper towel-lined tray.
Top each crispy rice round with mashed avocado and ceviche.
Spike ceviche with a splash of tequila if desired.