What can I use instead of clam juice?
Fish sauce! I think the clam juice is probably already a substitute for fish sauce anyway, so it should make a very good substitute. (If you look up recipes for Thai beef salad you'll find tons of things with fish sauce, and probably not much with clam juice.)

You probably want to use less, though, maybe starting with 2-4 tablespoons, though I've seen recipes using more.

It should be fine for the dietary restriction too; it's just made with anchovies, not an unknown blend of seafood, but of course check the label just in case.