Gantry mills can 'Crab" or "rack", not only during basic movement, but much worse during cutting. This is the primary reason I avoid such designs. It is much easier to have a machine that looks like a gantry, but the X axis moves on ways. This design makes the system as a whole much more rigid.
However, for a gantry system, the approach you suggested is doable, but you have to allow for clearance from one side of the machine to the other for the shaft. The other approach, depending on the controller software, is to use two motors, one on each side that are "slaved" together to act as one. While a shaft and gearing might seem cheaper, it may be cheaper to use two motors.
Hope this helps a little bit.