Counting in scores is not strictly the same phenomenon as the units-before-tens count, but does seem to share some of the same "flavour". It appears in formal speech in, for instance, the Gettysburg Address ("Four score and seven years ago our fathers brought forth ...") and in the biblical "three score years and ten" noted by @Benjol).
In British literature of the interwar period (this post is too informal and time too short for me to investigate sources, but I'm thinking of the Swallows and Amazons books by Arthur Ransome and Cold Comfort Farm by Stella Gibbons as good prospects), both counting in scores and the one-and-twenty forms would seem to be noted as low-status rural dialect markers. Another literary instance, Poem XIII of AE Housman's A Shropshire Lad, "When I was one-and-twenty" (1896) is also rural in setting. Lincoln's use thirty years before was probably something of an archaic rhetorical flourish as well.