This is what Jasper White (the king of NE cuisine that you like so much
"What's the Deal with the Grit?
Because they live on the ocean floor, steamers contain sand, which should be purged before cooking. (Those from mud flats, rather than sand, will be less gritty.) The traditional method is to soak them in salted water with a little cornmeal, supposedly encouraging them to spit out the grit. But White calls this method "useless — it doesn't do anything." Instead, he recommends repeated tossing in successive pails of cold water until the water remains clean. This can take as many as six or seven washings; handle the steamers gently to avoid cracking their shells. When submerging the steamers in the water, watch for any that float — this means that they're already dead and should be discarded. (Note that when preparing mussels, the opposite is true: They clamp shut tightly, trapping air in the shell, and therefore should float when alive. Discard any that sink.)"
"1. Fill two large pots (or two sinks) with cold water. Place the clams in one pot of water, discarding any dead ones or clams with cracked shells. Gently move them around in the water and let them soak for a few minutes, then lift them out and place them in the other pot of cold water. Rinse the first pot and fill it again. Move the clams around again, then transfer them back to the clean pot. Continue to switch the clams back and forth, letting them soak for a few minutes each time, and then lifting them out of the pot, until the water remains crystal clear. The process should take four or five soakings."