In a medium bowl, toss the pineapple rings with the onion, spices and 1/4 tsp. salt.
In two skillets, cook the bacon over medium until just crispy, about 12 minutes. Drain the bacon on a paper towel-lined plate. Crack the eggs into one of the skillets. Fry in the bacon fat over medium until the whites are set, 2 to 3 minutes; season the eggs with salt and pepper and transfer to a plate. Pour off all but 2 tbsp. of the drippings from the skillet.
Increase the heat to high; add the pineapple mixture. Cook, stirring once, until the pineapple rings are just browned, 3 to 4 minutes.
Spread mayo on each slice of toast. Divide the lettuce, bacon, pineapple mixture, avocado and eggs among 4 toast slices; top with the remaining toast.