Thanks a lot for all the tips everyone, never ceases to amaze me how willing this community is to help a stranger think through something like this. In one of my darkroom books, I found this image that's pretty close to the layout of my closet. You'll see that I've highlighted in red where the door actually is at our house, so it's slightly different. I like the idea of putting shelves next to the angled wall under the stairs.
That is, by far, the better layout. It should be relatively easy to move the door if the wall is non bearing. Even if it is a bearing wall, cutting an opening and installing the door on the side is just a matter of installing an appropriately sized header over the new door opening, and doubling up the studs supporting either end. If you can do it yourself, it would be very cheap, but even if you have to hire a home improvement contractor, it's a pretty cheap job if you reuse the original door and frame.
Andy

