Place pork tenderloin in a slow cooker; add onion, garlic, 1/2 cup barbecue sauce, and 2 tablespoons vinegar. Cook on low until meat shreds easily when pierced with a fork, 5 to 6 hours or high for 3 to 4 hours. Remove meat and shred; chop. Add back to barbecue sauce mixture, and stir well. Let cool to room temperature. Drain meat.

Meanwhile, toss red onion with salt and 1/2 cup water in a bowl. Let stand at least 1 hour, stirring occasionally. Rinse and drain well.

To make sushi rolls, place bamboo sushi rice mat on a work surface with plastic wrap. Open a nori sheet and lay it, rough side up, on the mat. Wet hands, and spread 1 cup sushi rice in an even layer on the the nori to within 1/2 inch of edges. (Wet your hands to work with sticky rice, but the nori sheet needs to stay dry.)

Arrange about 1/3 cup pork in a strip down the closest long side of the nori sheet, about 2 inches from edge. Lay a few slices of red onion and about 5 strips cucumber on the pork.

To roll, use the edge of the mat to nudge edge of nori sheet over filling; continue rolling up the nori wrapper tightly with the rice and filling. (The mat will help keep equal pressure on the roll for it to roll up evenly.) When you reach the end, moisten the edges with water to make the nori stick. Place, seam-side-down, on a cutting board. Repeat with the remaining nori sheets, sushi rice, and shredded pork barbecue.

Slice rolls with a sharp knife. Arrange slices on a plate; sprinkle with sesame seeds. To make dipping sauce, stir together remaining 1/2 cup barbecue sauce, and remaining 2 tablespoons rice wine vinegar, and season with soy sauce, if desired.

Place rice in large bowl and cover with cold tap water. Swirl rice in water; pour off water and repeat 2 or 3 times or until the water is clear. Drain rice well in a colander.

Place rice and 2 cups water in a medium saucepan; bring to a boil over high heat, uncovered. Cover, reduce heat to low, and cook 15 minutes. Remove from heat; stir, then let stand, covered, until liquid is absorbed and rice is tender, 5 to 10 minutes.

Meanwhile, combine rice vinegar, sugar, and salt in a small glass bowl and microwave on high until hot, 30 to 45 seconds. Transfer hot cooked rice to a large wooden or glass bowl and pour the vinegar mixture over. Fold thoroughly to coat each grain with mixture. Let cool to room temperature.