3ds Max :: Bend Modifier / Plane To Sphere

I'd like to use the bend modifier to transform a square plane into a sphere with a diameter equal to the side length of the original plane (to reproduce the approach for UV mapping a sphere described here).
 
I've been able to bend a vertical, square plane into something very close to a sphere using two bend modifiers (the first bending the x axis by 180 degrees with a direction of 0 degrees and the second bending the y axis by 360 degrees with a direction of 90 degrees). It's necessary to move the center of the second bend modifier to obtain a sphere.
 
However, there are two problems with the result: the diameter of the sphere is not equal to the side length of the initial plane and it's difficult to position the center of the second bend modifier such that the sphere doesn't have holes at its poles.
 
The first problem occurs because (as far as I can tell) the bend modifier assigns its gizmo an initial scaling such that the object to which the bend modifier is being applyed is bent but not stretched. This is reasonable default behaviour and applying an FFD 2x2x2 modifier after the first bend modifier allows the (now bent) plane to be scaled such that the height of the sphere that ultimately results equals the side length of the initial plane. However, when the second bend modifier is applied, there doesn't seem to be an easy way to precisely position its center such that the sphere's width equals its height (the next step would be to weld the vertices at the two poles). This is also the cause of the second problem since positioning the bend modifier's center correctly would also remove the holes at the poles.I've attached a max file (in a zip file) for reference (also see the left-to-right sequence in the image below):

- Plane001 is the initial square plane
- Plane002 is after the first bend modifier has been applied
- Plane003 is after adjustments have been made with the FFD modifier
- Plane004 is after the second bend modifier has been applied
- Plane005 is after the center of the second bend modifier has been adjusted.