Sprinkle 1 teaspoon salt over cucumber slices; let stand 1 hour. Drain slices on paper towels, pressing to remove excess liquid. Finely chop cucumber; combine with remaining package of cream cheese, mixing well. Chill.
Trim crust from bread. Cut each loaf horizontally into four 1/2-inch-thick slices. Save remaining bread for other uses.
Spread softened butter on each slice of bread. Spread avocado mixture on bottom slice, pimiento mixture on second slice, and cucumber mixture on third slice. Stack slices, and cover with fourth slice. Wrap each loaf in waxed paper and a damp towel. Chill at least 5 hours. Slice each loaf in half lengthwise and in 12 slices crosswise.