Answered: Joystick Stand

Our driver wanted to try out driving our robot using WASD controls with the buttons on the joystick, and found that it was actually a lot easier for him, but it was hard to hold up the controller in the right orientation.

Would we be allowed to build a stand (either out of vex parts or non vex parts) to hold the joystick that we could use during matches in competitions?

Yes, this is legal, provided that the event has room for this sort of device.