The only thing that will change the stiffness of a soundboard is if you change it's dimensions in length, width, or height. It's math, you cannot have an opinion of it, it's a solid fact
Don't confuse stiffness with strength:
https://www.setareh.arch.vt.edu/safa..._strength.html
Arching has it's own physical proerties too but it's my understanding that we luthiers do it more for dealing with changes in humidity than say building an aqueduct like the Romans did with arched structures for strength.