Well, not sure if I was very clear but I moved away from the 1/16ths system after I was dissatisfied with the matching quality.
I switched to a system where each tile has 2 terrains, and 4 values for each edge indicating the percentage of the first terrain to the total going from upperleft -> bottom right. (In the case that the first terrain is on the right / bottom part of the edge, you can use a negative value).
Thus the black/white example becomes (if I use terrain1, terrain2, N, S, W, E for the format):
B,W,100,0,0,100
That still doesn't give great results (because some of the tiles have to go together like we said).
So the real issue is, we need to find a way to account for this in code. Perhaps 'groups' of some sort that specify "A is a valid transition but only with B to the right of it," that sort of thing.