If you make a bar 20% wider it will be 20% stiffer (in vertical direction). No "cubes" involved here.

But if you make the same bar 20% higher it will be 1.2 x 1.2 x 1.2 times stiffer (also in vertical direction). That's 1.728 times stiffer, or 72.8% stiffer.
Oh, and btw: this is going to be a beautiful guitar. I agree that this archtop model by itself is aesthetically very pleasing (if it's sexy or not depends a lot on each guitar, but this one will be it for sure!)