You don’t need math. Just place the parts where you want them in CAD and drop a sketch ontop of the assembly to form your custom plates. Place the VEX C-chan such that the distance of 0.5" between centers is maintained. Do this for each “grid”, the grid that is normal and the grid that is 45 degrees offset. Don’t worry about trying to otherwise align the two grids, just make sure the 45 deg offset grid is symmetric to the origin. Doesn’t matter if the corner grids align with each other, as long as they are locally 0.5" that’s fine. You don’t even have to do that if you don’t want to, but you live with those decisions.
Best to only CAD one corner and pattern it. In Fusion, place the parts, including the pre-cut c-chan that goes in the corner at a 45, use the align tool to position things then move them locally in 0.5" increments, make a new component like “Corner Bracket” and start it as a sketch on the existing design. Make the sketch, extrude it and then make the 4 or 8 copies (best to have two plates per side, one top, one bottom) and you’re done.
What to make it out of? That depends on the competition you are targeting or if this is just for funzies. I would CNC 1/16" aluminum, but that’s probably not VRC legal.
Also, it’s better to use round holes rather than trying to replicate the square holes. You’ll have less play. Use the hole tool in Fusion and set it for a clearance hole for an 8-32 thread. If you want a more “vex like” fit, use the measure tool to find the width of a VEX hole and use that as the diameter instead. In general VEX has 0.007" slop on either side of the hole.
If you want to go pro-mode, take the 45 degree c-chan and make sure it’s an odd number of holes, center that hole on the origin, and move it 0.5" out from the origin until you are happy with it’s final position. This aligns the corner grids with a common 0.5" spacing. You will 99.9% likely not need or use this, but your OCD will make you feel good about it.