Unless the molecular axis is fixed in the laboratory frame, intrinsic structural information of molecules can be averaged out over the various rotational states. The macroscopic directional properties of polar molecules have been controlled by two fs pulses with an optimized delay. In the method, the first one-color laser pulse provokes molecular alignment. Subsequently, the molecular sample is irradiated with the second two-color laser pulse, when the initial even-J states are aligned, and the odd-J states are anti-aligned in the thermal ensemble. The second pulse selectively orients only the aligned even-J states in the same direction, which results in significant enhancement of the net degree of orientation. This paper reports the results of simulations showing that the two-pulse technique can be even more powerful when the second pulse is cross-polarized. This study shows that the alignment and orientation can be very well synchronized temporally because the crossed field does not disturb the preformed alignment modulation significantly, suggesting that the molecules are very well confined in the laboratory frame. This cross-polarization method will serve as a promising technique for studying ultrafast molecular spectroscopy in a molecule-fixed frame.