This is the time that you need to start using an FEA program like Fusion or alternately some experimental measurements like you did yesterday.
I've tried Fusion360 a time or two and have stepped away frustrated. I understand that there are plenty of tutorials available, but it's just so damned complicated. I taught myself to use SketchUp years ago when it was still associated with Google. I know it's a FAR more limited CAD app, but as it stands it's what I know relatively well. There's another web-based app that's supposed to be far more capable, but I can't recall what it's called.

Get some materials together and start making some more precise measurements and allow those measurements to direct your design.
One handicap is that I lack detailed information on the aluminum extrusion that I have. I can only say what its dimensions are and that it's almost always anodized on the exposed face(s). I couldn't tell you if it was 6061 or some other alloy. Some of it is relatively new and some of it is decades old.

When it comes to the gantry, the force applied is primarily to the tool at the end of the spindle doing the cutting, right? I can visualize the spinning tool creating quite a bit of rotational torque as it engages the material. This would be amplified if it's a "hard" material or has inconsistent density like knots in wood. Other than that though, are we trying to apply significant horizontal force as the tool is cutting? If I'm running a router by hand, I don't push the tool hard to its limits; if the tool is sharp it's not necessary.

I've been trying to find images that display the typical stresses on a gantry so I can try to get my head around how to design mine. Sadly, we just found out that my wife's losing her job, which obviously cuts well into any disposable income for the household. While I'll still be designing and redesigning, buying the pricey CNC pieces is on indefinite hold.