Alright!  If I get a chance tomorrow, I will try to quickly draw the design in my head.

I am going to use the headstock casing from my broken spindle to hold the syringe.  This piece is convenient because it already mounts to the Sherline Mill.  I will then mount the motor and axis screw directly to the headstock casing.  Finally, I will mill rods to go between the saddle nut on the axis screw and the piston...

I have a thin sheet of metal to act as the build base.

Fowler