jmho, ymmv, but i cant help but think that that design would be many fold more rigid if:
the builder had used rectangular tubing on the base of the gantry sides that extended to the top and bolted to it all the way. even if the rect tubing was open on the back face to clear the stepper. a pair of triangular gussets on both sides of the machine added now running from the tops of the rect tubing to the tops of the endplates would be much more rigid. i might even tie the 2 backsides of the triangle hypotenuses together with 2 straps ea for more rigidity. an "x" shape would be better.
a sawcut aluminum "x" connecting the 4 corner edges of the alum endplates would help too. even a solid plate but that would be more cumbersome. a pair (front and back) would help even more so. maybe the back not needed since it looks like the spindle mount hangs on extruded shaped tubing. i might put a brace in the middle of the extruded tubing linking them, and check that the distance from guide tube to guide tube is the same in the middle as it is on the ends.
id bet the machine would hog faster, be more accurate in corners finishing, and run quieter and give better tool life. again, jmho, ymmv. im not a machine builder, but i did stay in a holiday inn express.....heh....on a more serious note, i have a cnc bridgeport in the garage, not so rigid, and run a large horizontal workcenter for my day job, very rigid, trust me rigid is good. perhaps your demands dont justify this, just trying to help.
ken