My community college library where I work, interestingly, has William Livingston's papers (and unlike the David Library, they let me check the work out).
Under the pseudonym "Cato," Livingston wrote on Church-State issues. In that year he makes arguments arguably using the rhetoric of "separation." Interestingly, Phillip Hamburger's otherwise thorough work misses Livingston.
Unfortunately, I can't, as I like to do, copy, paste, and link to a public domain work. So I'll have to actually write his words out. From a work dated February 4, 1778, he writes:
Hence the motley junction of king-craft and priest-craft (the most fatal engine ever invented by Satan for promoting human wretchedness) usually called the alliance between church and state, but in reality a most atrocious conspiracy between two public robbers, for sharing between them the plunder of nations; and for that purpose mutually supporting and supported by each other. And hence all politico-ecclesiastical establishments under pretence of promoting religion, by kings who generally have none, and church dignitaries who seldom care for any.
Next we will see Livingston making arguments that strikingly parallel those made in James Madison's Memorial and Remonstrance.