Cecil,
I just had a look inside my dot matrix printer. It has a timing belt supported by a toothed wheel at each end with the print head attached to the centre of the belt. One toothed wheel has a gear reduction to the motor. This looks like what you are trying to do. You will probably need a belt on each side of the X axis connected by a jack shaft. The other issue would seem to be some sort of support to reduce belt sag when the carriage is at it’s extremes. Slides attached to the gantry with magnets and "left behind" at preset intervals to support the belt may work.
Steve
www.tac-pro.com