Oh well, it's a learning experience fer sure. Probably the best way to transport & keep them would be in seawater taken from where they were dug. If it's hot out then placing them in a cooler would be helpful, though I have found them to be quite resilient from temperature change for a good period of time. Icing will of course dilute the seawater (unless you have seawater ice!).

My favorite pasta recipe for butter clams is as follows:

Heat slowly in a large iron skillet or Dutch oven:

1/2 cup olive oil
add:
1/4 tsp (or too taste) crushed red pepper flakes,
1 large chopped onion,
3 large cloves mashed & chopped garlic,
a generous bunch of fresh or dried sweet basil,
1 Tbls oregano,
salt & pepper to taste.

Cook slowly about half an hour. (Optional: after about 15 minutes add sliced mushrooms).
Add 1/2 cup or so of clam nectar (or drained liquid from 2 cans clams). I also add 1/4 cup or so dry white wine at this point.
Increase heat a little so liquid will cook down to oily stage again. Cook: 1 pound box of spaghetti or linguine with salt and a few drops oil.
Five mins before pasta is done, add:
1 cup (or more!) chopped cooked clams or 2 cans drained canned clames with
1/2 cup chopped parsley, and
3 Tbls freshly grated Parmeson or Romano cheese.

Simmer clams 5 minutes at low heat (careful not to overcook clams, they get tough). OPTIONAL: add small can or bunch of precooked small shrimp.
Slp drained pasta into skillet/pot with sauce. Toss pasta & sauce together over low heat a couple of minutes. Slather plenty of cheese over top and serve from skillet/pot.