An interesting idea. I'll be watching your build thread.
Since X is a rotary axis, I think it's going to require a translator program to use standard cartesian G code. I don't know of any controllers that would do this natively, but such a thing may exist. To create a straight line, you would need to calculate the X angle and Y distance for a series of points along the desired path. The inverse of converting arcs to lines in a normal system. Not difficult, just simple trig, but would require a program to make it practical. The translator could output standard G code that any controller could read, but the file would be considerably longer than the original G code file. Overall very doable.
Mechanically to minimize the X backlash, I think you will want to drive the X axis from the outside end of the arm. Maybe a 1/4 circle rack attached to the building structure and the pinion on the motor attached to the outboard end of the arm. Something like that.