Because of the depth of the cabinet, the disk cases will stand on edge in
rows running front to back. Everything is fine and dandy when the drawer is
filled to capacity, but I'm looking for ways to keep a partial row of disks
from toppling over as the drawer is opened and closed.

A few things I thought of...
1. It'd be a bit complicated, and might affect the size/design/
construction of the drawer, but you could do a file-cabinet type thing
and put a length of threaded rod just under the floor of the drawer,
or along each side. Many file cabinets I've used have a piece of rod
with a friction-fit plate of some kind that holds up an end piece to
keep file folders upright. A piece of threaded rod with some nut/
upright holder contraption might be easier if you didn't want to
design a friction-fit system. (Sorry if this is just confusing - hard
to describe, but look at an old metal non-hanging file cabinet and
it's not a complicated concept).
2. You could drill holes for pegs along the sides or bottom of the
drawer, and use removable dowels to hold the back DVD upright. Kind
of like the adjustable shelf supports. You could either do both sides
and the bottom, so 3 short dowels would hold up the DVD, or 1-2 rows
of holes on the bottom with longer dowels, or holes just on the sides
with some kind of DVD-sized panel to create a back.

Just a few ideas, let me know if I didn't explain them clearly,
Andy