Special equipment: 8 sake cups and 8 sake boxes
For the citrus-infused sake: Peel large strips of zest from the lemons and limes and put in a large Mason jar or other container. Pour the sake over it and let it sit for at least 1 hour (and up to 1 week covered).
For the octopus: Bring a large saucepot of water to a boil. Add the salt, scallions, ginger and 1/2 cup of the sake. Let simmer for 5 to 10 minutes to infuse the water. Quickly blanch the octopus in the simmering water, 10 to 15 seconds. Remove the octopus to a plate to cool. Save the ginger for the garnish.
In a small bowl, combine the light soy sauce, sugar, vegetable oil and remaining 1/4 cup sake. Stir until the sugar is dissolved.
Heat a grill or grill pan to high. Brush the octopus with the sake-soy marinade. Grill the octopus until just cooked, 2 to 3 minutes on each side; the tentacles will curl and be slightly charred and the octopus will be opaque.
With a lemon zester, zest threads from the reserved ginger. Toss with some of the sake-soy marinade. Heat a small skillet to high heat. Saute the ginger threads for 10 to 15 seconds.
To serve: Place a sake cup in a sake box on one side of each serving plate. Fill each sake cup with some of the citrus-infused sake. Place a small mound of kosher salt on the corner of each sake box. Place a shiso leaf, if using, in the middle of each serving plate. Place a grilled octopus on each shiso leaf. Place some ginger threads on each octopus as a garnish. Use the zester to cut long threads of zest from the lemon and lime. Place some lemon and lime threads on another corner of each serving plate as a garnish and serve.