Your link doesn't go where you say it does.
The packaging machinery company I work for makes a device that uses a cable system to keep both ends of an assembly aligned as it moves. It works quite well, and lasts literally millions of cycles at rates up to about 60 strokes per minute. So the concept is certainly valid. However, in our case, the accuracy requirement isn't nearly what a CNC router would need. I wonder what the extra mass of the cable and pulleys would do in a transient situation? I suspect it would work if you use good quality pulleys, like those used in aircraft control cable assemblies. Even so, there will be an initial break-in period where the cable will stretch a little. So you'll have to build in some tension adjustment and keep it adjusted with some frequency. Fix your link so we can see the system you're referring to.
I wouldn't use brass for the gantry tube. Depending upon alloy, you get 1.5-2 times the stiffness at 3 times the weight. You're better off increasing the size of the gantry tube by an inch. For example, if you're worried about vertical deflection, going from 1-1/2 x 3 to 2 x 3 will almost double the vertical bending stiffness, and increase torsional stiffness by about 40%. Such a change only adds minimally to the mass. Of course, this ignores the significant vertical stiffness contribution of the steel guide bar, which would also have to get larger and heavier.
Widening the bearing blocks would also help with the gantry alignment. But, if you're going to go the cable route, you probably don't need it. Keep in mind, your base and X rails will have to increase in length for the given work envelope, so it's definately diminishing returns at some point.
No signature I would write will fit on only two lines.