If desired, save some small slices of papaya, carrot, and bell pepper to make garnishes like flowers, stars, crescent moons, etc.
Peel the papayas. Cut them open and scrape out the seeds. Shred or grate the papaya. Place the shredded papaya in a large bowl. Sprinkle over the 1/2 cup kosher salt and mix well, to thoroughly coat papaya. Allow to sit for at least an hour (longer is better; halfway through, mix well again).
Meanwhile, prepare jars. Use six 1-pint jars or combination. Sterilize jars: In a large pot with a rack on the bottom, place clean jars right side up. Fill with water to cover jars by 1 inch. (If hard water, add a splash of vinegar so jars don't dry spotty.) Bring to the boil, then boil for 10 minutes and turn off. Put clean lids in the pot to get warm. Leave jars and lids in hot water until needed.
Prepare the other vegetables. Shred or grate carrots. Slice tops of jalapenos and remove seeds. Thinly slice red onion, bell pepper, jalapenos, and garlic (mandoline is very useful here). Peel and julienne the ginger. Combine all vegetables in a large bowl. Add the raisins. Mix well to combine.
Make the brine. Combine the kosher salt, sugar, and vinegar in a pot. Cook over medium heat, only long enough to dissolve the salt and sugar. Turn off heat and allow to cool a little, until it's still warm but you can touch it. (This makes a bit too much brine but otherwise it's not enough!).
When papaya is ready, transfer it to a colander, and rinse it well under running water. Turn it onto a kitchen towel or cheesecloth, and squeeze tightly to get all the water out of it. Add to bowl with vegetable mixture. Pick the papaya apart so it doesn't clump. Mix well with other vegetables.
Place a kitchen towel on the counter. Remove jars from hot water, drain, and place on towel, right side up. Carefully fill with mixture; pack a little tightly; leave about 1/2 inch at the top. Fill each jar with brine, leaving 1/4 inch space at the top. Gently tap each bottle on the counter, and stir with a chopstick to remove any air bubbles.
If adding garnishes, use the chopstick to poke them down the sides of the jars.
Wipe jar tops clean. Place lids on jars, and tighten. (If using canning lids, place lids and hand-tighten rings.) Allow to cool. Keep refrigerated.