Welcome to EDABOARD
any way you have to use 3 wires with ground as third. please manage to have a 3 way ribbon cable and use middle wire as ground. Also, try to keep minimum wire length.
you might , i suppose, have used twisted pair .
instead , use one twisted pair with second (mate)wires as ground , for each direction of signal. these pairs need not be twisted again among themselves.
alternately use two shield cables with their shields as ground.
First method might it self reduce the cross talk. Hope to hear again