That ratio is from a Stagea (= 4.083:1). GT-R is 9 (pinion) and 37 (crown wheel).
Get a replacement diff (GT-R, GTSt, Stagea, doesn't really matter), and swap the crown wheel onto your existing centre, and the pinion into your existing housing. That way, input and output bits will still match up. If you get a differential specialist to do it, they can set up the backlash correctly at the same time.
BTW, the ratio is generally stamped somewhere on the crown wheel ("teeth on c/w" : "teeth on pinion") - saves a heap of tooth counting!