I remember reading something to this effect (in English) on the internet years ago and decided to take a shot at translating it.
I didn't know of the contracted form, but on looking it up I see it now. However, in Teach Yourself Ancient Greek, page 171 it says that the second member of the comparison must be the same as the first, citing the example Σωκράτης σωφότερός ἐστιν ἢ ἐγώ.
White's book says in #867 that the dative of manner is used to denote the degree of difference. Therefore I think you're right about τέτταρσι
; I simply hadn't gotten that far yet in my reading.