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.