My mistake. I used for the area of a circle [itex]A=\pi d^2[/itex] (i.e. squared the diameter instead of the radius). That means I was out by a factor of 4 on both the areas. But that doesn't affect the ratio of the areas, which is still 1.8, as I said.
Magnification isn't determined by the focal ratio. The magnification you get is the focal length of the scope divided by the focal length of the eyepiece. Essentially, magnification is not the biggest issue for a telescope, anyway. Often the best views are at lower magnifications (depending on what you're looking at, of course). But changing eyepieces can give you whatever magnification you want, up to a practical limit determined by the scope aperture.
I'm not sure why you think things will be dimmer in a larger scope. Given the same magnification, things will always look brighter in the larger scope.