Welcome to the forum, Mike.
Were the new fixtures installed by a pro? I ask because any experienced remodeler knows to use silicone instead of plumbers putty to set fixtures like that on cultured marble. They do make oil-less plumbers putty, but some installers also avoid that out of an abundance of caution.
I’ve not had any luck removing a stain like that. If the remedies you mentioned improve things, that means the stain is a surface contaminant, rather than a stain that’s gotten into the surface.