Transposing every matrix does not change anything. If you throw two matrices X & Y as input, then the coordinates for each Z-value is obtained from those matrices, i.e. Z(1,1) is plotted at [X(1,1) Y(1,1)]. If you transpose each matrix, then the coordinates for each Z remains the same. If you are instead throw only the Z matrix as input to contourf, then transposing it works because the Z-values are plotted against their index, i.e. Z(1,1) is plotted at [1 1].
I suppose this is what you are trying to do:
[xc,yc]=contourf(new_Y,new_X,new_Z);
