You can make "saltwater" for a second rinse once you get home, 1/4 - 1/3 cup salt per gallon of water. I used to just put them in a cooler, no need for the fridge as you can toss some ice cubes in as well. I have had mixed results with the corn meal. The warmer the water the more frequently it needs to be changed though as they can run out of oxygen
When I do clams now, I steam them, pop the meat out, pinch off the stomach, rinse, toss back in a bowl, add garlic and butter, microwave, and eat. No grit at all.