Can anyone explain the difference in design / quality issues with fixed vs. variable f-stop zooms, and why are the fixed f-stop generally so much more expensive.

Good question... There are many reasons. For underwater, constant aperture zooms focus faster and are sharper. For a nice explanation on the pros and cons check this page:

http://www.planetneil.com/faq/pro-lenses.html

The difference in cost comes from the fact that more glass (and better quality glass) is necessary to maintain the same aperture (as opposed to darkening the entire scene) as you zoom in.

The basic advantage with a fixed stop zoom underwater is that apertures remain constant when zooming which may result in less adjustments when setting manual flash power levels. Some are also classed as 'pro' lenses (Canon designate this by the 'L' designation, Nikon by those which they will apply priority repair status to for pros!) and these usually (but not always) have better optical characteristics/build quality. Of course you tend to pay a premium for this.

To expand on what Luis explained, to maintain a fixed aperture as the zoom lengthens, you need larger glass elements: when you zoom in, the focal length increases, and since the aperture is expressed as a fraction of the focal length, the larger that focal length gets, the larger the glass needs to be to maintain this large aperture. Clear so far?

Now, zoom lenses focus (autofocus or manual) at the largest available aperture for a given focal length. So, the other big advantage of a constant aperture zoom is that you'll always focus at the largest, and therefore brightest, aperture available.