Place zucchini and onions into a large bowl and cover with water. Add salt and stir until dissolved. Let vegetables soak for at least 2 hours, then drain and transfer to a large pot.

Bring sugar, vinegar, mustard seeds, celery seed, turmeric, and yellow mustard to a boil in a saucepan. Pour mixture over drained zucchini and onions; let stand for at least 2 more hours.

Place the pot with the vegetables, spices, and pickling liquid onto the stove and bring to a boil. Boil for 3 minutes.

Inspect three quart-sized jars for cracks and rings for rust, discarding any defective ones. Immerse in simmering water until vegetables are ready. Wash new, unused lids and rings in warm soapy water.

Pack vegetables into hot, sterilized 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 lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the 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 10 minutes.