Put the clams and their juices in a mesh strainer or sieve lined with a few layers of cheesecloth, or a large coffee filter over a medium bowl. Meanwhile, fill a large bowl with cold water. When the liquid has drained from the clams, remove and discard the cheesecloth or filter and leave the clams in the strainer. Reserve the strained juice.
Position the strainer in the bowl of water so that the clams are completely submerged. let them sit for a few minutes, stirring occasionally so that any grit can fall to the bottom of the bowl. Lift the strainer and clams out and discard the gritty water. Place the clams on a cutting board, pat dry with paper towels, and gently run a knife through to break up any larger chunks. Set aside while you make the chowder. (Also, take a moment to rinse and dry the strainer; you'll need it in a bit.)
Render the salt pork in a large heavy-bottom pot over medium-low heat, until just crisp and golden brown, 5-7 minutes. Add the onions and celery and cook with the pork and its rendered fat until tender but not browned, 4-5 minutes. Sprinkle in the flour and stir with a wooden spoon to incorporate and cook out the raw flour taste, about 1 minute.
Add the potatoes, 1 teaspoon of the salt, the pepper, bottled and reserved clam juices, the kombu, and bay leaves. Stir until fully combined and no lumps of flour remain. Bring to a boil, then reduce the heat to low. Cover and simmer, stirring occasionally, until the potatoes are soft, 15-20 minutes.
Remove and discard the kombu and bay leaves. Add the half-and-half and 1 cup of the clams and leave over low heat to gently warm while you fry the clam topping.
Heat the oil in a medium saucepan over medium-high heat and attach a deep-fry thermometer. Bring to 375 F, then reduce the heat to medium-low. Have a plate lined with paper towels and a slotted spoon or spider standing by.
Combine the cornmeal, cornstarch, 1/2 teaspoon salt, and a pinch of pepper in a medium bowl. Add the remaining clams and toss to coat. Place the clams in a strainer and shake off the excess cornmeal mixture. Working in batches, carefully place half of the clams in the hot oil and cook for 30-60 seconds. Carefully remove with the slotted spoon and place on the paper towel lined plate. Repeat with the remaining clams. When they're all out of the oil, season with extra salt and pepper, if desired.
To serve, ladle soup into a bowl and top with the fried clams and the celery leaves.