Peel cucumbers, halve lengthwise, and scrape out seeds with a spoon. Cut halves into 1/4-inch half-circles and place into a glass or ceramic crock. Dissolve pickling lime in about 1 quart room temperature water; pour over cucumbers, then add additional water to cover cucumbers by 1/2 inch. Let stand at room temperature for 24 hours.

Drain cucumbers and rinse well with cold water. Place into a large stockpot and cover with cold water. Let stand at room temperature for 3 hours, then drain and rinse again.

Return cucumbers to the stockpot. Add 1 cup vinegar, food coloring, alum, and enough water to cover by 1/2 inch. Bring to a boil. Reduce heat to a simmer and cook for 2 hours. Drain and let cool a bit before placing into the glass or ceramic crock.

Stir together sugar, remaining 2 cups vinegar, 2 cups water, red hot candies, and cinnamon sticks in a saucepan over medium heat until sugar and candies dissolve. Pour over warm cucumbers. Cover and let sit for 8 hours to overnight.

Pack pickles into hot, sterilized pint jars, filling to within 1/4 inch of the top. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe the rims with a moist paper towel to remove any residue. Top with the lids and screw the rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower the jars 2 inches apart into boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 15 to 20 minutes.

Remove the jars from the stockpot and let rest, several inches apart, for 12 to 24 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area. Refrigerate any jars that do not seal.