Shred half of the Monterrey Jack cheese to regular shred. Shred the other half to fine shreds. This creates a creamier texture to the pimento cheese spread.
Shred the cheddar cheese to regular shred size.
Combine the cheeses with the mayo, pimentos, sugar, Worcestershire, pepper, and paprika. Combine very well.
For each sandwich, toast two pieces of white bread. Spread a thick layer of pimento cheese spread onto the bottom piece. Top with two strips of bacon, lettuce and tomato.
Slice into halves diagonally, or quarters for serving a crowd.