In a small bowl, whisk together the rice vinegar, coconut sugar, and sea salt until dissolved, then gently fold into the warm cooked sushi rice and let cool.
Slice the sashimi-grade salmon into long, thin strips and butterfly the cooked shrimp by cutting along the back without slicing all the way through.
Place one nori sheet on a bamboo rolling mat with the rough side facing up and the long edge closest to you.
Using damp fingers, spread half of the seasoned rice in a thin, even layer over the nori, leaving the top 1-inch border empty.
Arrange the salmon strips, half of the julienned cucumber, and half of the carrots in a horizontal line across the center of the rice.
Lift the edge of the mat closest to you and roll the nori over the filling, pressing firmly to create a tight cylinder.
Lightly dampen the empty top border of the nori with water to seal the roll, then repeat the process with the remaining ingredients, using shrimp and avocado.
Use a very sharp, moistened knife to slice each roll into 8 uniform pieces and serve immediately with tamari, wasabi, and pickled ginger.