Begin the salt brine on Day 1. Wash the cucumbers. Cut a ¹⁄₁₆-inch slice from the blossom end of each cucumber and discard it, leaving approximately ¼ inch of stem attached. Place the whole cucumbers in a clean, food-safe one-gallon container. Combine ¼ cup canning salt with 2 quarts water and bring to a boil. Pour the boiling brine over the cucumbers. Add a suitable cover and weight to keep the cucumbers 1 to 2 inches below the brine. Cover the container with a clean towel and keep it at approximately 70 degrees F.
Replace the brine on Days 3 and 5. Drain and discard the salt water. Rinse the cucumbers. Briefly boil the cover and weight to sanitize them, then return the cucumbers to the container. Combine ¼ cup canning salt with 2 quarts fresh water and bring to a boil. Pour the boiling brine over the cucumbers and replace the cover, weight, and clean towel. Repeat the entire process on Day 5 using the remaining ¼ cup salt and 2 quarts water.
Cut the cucumbers and add the vinegar syrup on Day 7. Drain and discard the salt water. Rinse the cucumbers. Briefly boil the container, cover, and weight to sanitize them. Cut the cucumbers crosswise into thick, even slices approximately 1 inch wide, then return the large pieces to the container. Place the celery seed and pickling spices in a small cheesecloth bag. Combine 2 cups sugar and 4 cups vinegar in a saucepan. Add the spice bag and bring the mixture to a boil. Pour the hot syrup over the cucumbers. Replace the cover, weight, and clean towel.
Add sugar on Days 8 through 13. Each day, drain the syrup and spice bag into a saucepan and reserve them. Add ½ cup sugar and bring the syrup to a boil. Remove and rinse the cucumber pieces. Briefly boil the container, cover, and weight to sanitize them. Return the cucumbers to the container and pour the boiling syrup and spice bag over them. Replace the cover, weight, and towel. Repeat this process once each day for six days, adding ½ cup sugar each day.
Fill the jars on Day 14. Prepare a boiling-water canner. Drain the syrup into a saucepan. Pack the cucumber pieces into sterile pint jars or clean quart jars, leaving ½ inch of headspace. Add the final ½ cup sugar to the syrup and bring it to a boil. Remove and discard the spice bag. Pour the hot syrup over the cucumbers, maintaining ½ inch of headspace. Remove air bubbles, adjust the headspace if needed, wipe the jar rims, and apply two-piece canning lids.
Process the jars. Place the jars in the boiling-water canner and process them using the time listed for your jar size and elevation (see notes below). After processing, turn off the heat and remove the jars according to safe water bath canning instructions. Let the jars cool undisturbed for 12 to 24 hours, then check the seals before storing.