Ribbon Cable Cross Talk - Is there a fix after the fact?
Can you change the ribbon cable, or insert an adapter to a higher pin-count cable? Consider what IDE/ATA did to increase bandwidth -- it was switched from a 40-wire cable to an 80-wire cable, with every other wire inside the cable tied to ground within the connector. A similar solution could apply here.

Alternatively, can you reduce the slew rate? At 1 MHz, your problem is likely to be less about the frequency of the signals themselves and more about their fast edges. A filter network on the transmit side may help.