Are all your citations in footnotes? Unlike the intext citations, which do not have any variation apart from the (Author, Year) and Author (Year) (or hide author or hide year) options, footnotes do have ref type specific templates for the citations. And footnotes also have the option to have a “short version” of the citations which you could have the full case name field replace by a field with the abbreviated case name, for subsequent references. Have you looked at Blue book-Law review for examples. It has a field for the abbreviated case name which is used in the short form of the footnote.