You cant see it, but in that last render showing the mdf spoilboard there is a metal structure of angle iron underneath supporting the table and tying the two sides together. I'll probably add a piece of tubing across the front and back of the machine as well or at least gussets on each corner if I decide the tube will get in the way. I ran a simulation on the gantry uprights as if you were pushing on it from the side (I think thats what you were meaning?), with a 50lb load the deflection was .004". I'll do the same study for the base of the machine next. I don't know why I keep using 50lbs it just seemed reasonable for cutting through wood. If anyone has a better idea of how much radial load is acting on a tool cutting into wood let me know.
edit: The base showed a deflection of .002", adding the .004" from the uprights gives a total deflection perpendicular to the x-axis of .006" with a 100lb force (50lbs distributed to each side of the gantry). Looking at the numbers you posted on that other thread this seems reasonable, my machine looks to be about half the size and has twice the deflection, makes sense. I'm not a machinist so these small numbers aren't as easy for me to grasp, I have to put it into terms I can relate with so .01" is about half the size of a piece of lead from a .5mm lead pencil. If I can get my machine to perform within those tolerances I'd be tickled.