Thanks again for all the replies and ideas, particularly the one on
easing the ends of the dowels. That helped tremendously.
I wound buying a pack of multi-purpose panel foam -- polystyrene. Very
inexpensive stuff. Having used a Kraft paper template for layout of
all the dowels, I simply transfered the hole locations from the paper
to the polystyrene, then drilled out the foam with a 3/4" forstner.
(Yes, little pellets of poly just about everywhere.)
I squared and glued up the top and bottom shelves to one side of the
cabinet and let them dry. Then, I threaded the 24 dowels through the
poly and into the pre-assembled side, moving the poly panel to its best
location. That held all dowels pretty much in place. Then it was just
a matter of gluing up the bottom to the other side and clamping it
loosely, setting all the dowels in place, until the top was glued and
set... then clamped it all home.
After it was dry, I simply broke pieces of the poly away... and cleaned
up the mess. Next time, I'll wait for more humid weather...
On another note... I didn't engineer the piece too well for the span.
Using 3/4" dowels over 33" span didn't hold all those CDs very well,
with each span sagging noticeably in the middle. It looked pretty bad.
To fix that, I took a spare rip of mahogany and planed & chamfered it
down to what I thought would be a minimal thickness and width, then
drilled out 1/2-holes for the front-most dowels. I simply popped the
piece vertically in the middle, setting it on the bottom shelf, and
snapped the 1/2-holes over each of the front dowels. No glue, no
nails, no nuttin'. It now sits there, supporting the dowels nicely in
the center, and looks just like a pre-planned center divider.