Put the tilapia in a medium bowl. Pour the lime juice over the fish and mix gently to combine. Cover with plastic wrap and chill in the refrigerator until the fish is white throughout, about 15 to 20 minutes.
Remove from the refrigerator and drain off the lime juice, gently squeezing the fish with your hands. Discard the lime juice. Add the tomato, cucumber, onion, and cilantro. Season with salt and pepper, to taste. Add the clam-tomato juice and the hot sauce and chile, if using.
Spread the tostadas generously with mayonnaise and top with the ceviche. Arrange the avocado slices on top of the ceviche and serve immediately with the lime wedges alongside.
Heat a grill or grill pan over medium heat.
Put the tortillas on the grill or grill pan, and let them dry out until they are crunchy. Purchased tostadas can be substituted.
The fish is easiest to dice when it is partially frozen; this also makes for a much cleaner presentation. Use a very sharp knife.