Drain the vegetables: Layer the squash and onions, salting each layer with kosher salt, in a large nonreactive bowl. Let stand in sink for 3 hours. Drain the squash and onions, transfer to a large colander and rinse well under cold water. Place a bowl over the vegetables, and add a couple cans of tomatoes or whatever you have on hand to weigh the bowl down to squeeze out as much of the water as possible.
Prepare the jars and lids: Wash all jars and lids thoroughly with soap and water and rinse well. Fill your canner with enough water to cover the jars by at least 1-inch and bring to a simmer. Using a pair of canning tongs, lower the jars in gently, tilting them to fill with the hot water. In a small saucepan, keep some water warm but not boiling; place the lids in the water. Have an additional kettle of water on to boil.
Make the brine: Bring the sugar, vinegars, mustard and celery seeds and turmeric to a rolling boil in a large nonreactive stockpot or Dutch oven. Add the squash and onions. Bring back to the boil, stirring gently. Remove from heat and allow to cool.
Make the relish: Transfer the pickles in batches to a food processor, and pulse until broken down to a fine, even consistency. Return the processed relish to a pan and bring back to a boil. Add the pectin, stir until completely dissolved and bring back to the boil for 1 minute.
Fill and close the jars: Using canning tongs, remove the jars from the canner, carefully pouring the water back into the canner. Set next to the relish in the saucepan. Turn the heat under the canner to high. Use a ladle to pour the relish into the jars through a canning funnel, leaving 1/2-inch headspace at the top. Run a clean chopstick around the inside of the jar to dislodge any trapped air. Wipe the rims of the jars with a damp paper towel. Place the lids on, and screw on the rings until just finger-tight.
Seal the jars: Using canning tongs, gently transfer the jars to the canner, taking care to keep them vertical. When all the jars are in the canner, there should be at least 1 inch of water covering them; if you need more, add water from the kettle until the jars are sufficiently covered. Bring the water to a full rolling boil, and process for 10 minutes.
Remove and cool: Using canning tongs, gently remove the jars from the canner and transfer them to a kitchen towel or cooling rack, again keeping them vertical. Do not set hot jars directly on to cool counter surfaces. Leave to cool, undisturbed, for at least 12 hours. If any of the jars do not seal when cool, reprocess using the method above, or refrigerate and use immediately.
Label and store: Add a label to the lid or side of your jar, noting the date it was canned. Remove the rings and store jars in a cool, dark place for up to one year. Refrigerate after opening.
Properly handled sterilized equipment will keep canned foods in good condition for one year. Making sure hands, equipment and surfaces in your canning area are clean is the first step in canning. Tips: Jars should be made from glass and free of any chips or cracks. Preserving or canning jars are topped with glass, plastic or metal lids that have a rubberlike seal. Two-piece metal lids are most common. To prepare jars before filling: Wash jars with hot, soapy water, rinse them well and arrange them open-side up, without touching, on a tray. To sterilize jars, boil them in a large saucepan, covered with water, for 10 minutes. Jars have to be sterilized only if the food to be preserved will be processed for less than 10 minutes in a boiling-water bath or pressure canner. To sterilize jars, boil them in a large saucepan, covered with water, for 10 minutes. Follow manufacturer's instructions for cleaning and preparing lids and bands. Use tongs or jar lifters to remove hot sterilized jars from the boiling water. Be sure the tongs are sterilized too: Dip the tong ends in boiling water for a few minutes before using them. All items used in the process of making jams, jellies, preserves and pickles must be clean, including any towels and especially your hands. After the jars are prepared, you can preserve the food. It is important to follow any canning and processing instructions included in the recipe and refer to USDA guidelines about the sterilization of canned products. Find Information information on canning can be found at the National Center for Home Food Preservation website: http://nchfp.uga.edu/.