i would not rinse the clams. strain and, yes, run the clam liquor through a coffee filter.
a couple of anchovies certainly won’t hurt for adding umami that robin gets from cheese. although i am with you and don’t like cream or cheese in this application.
it will benefit from a hit of acid though. do you have any rice vinegar? a splash at the end is nice. finish with red pepper flakes and fresh parsley.
