All,
I dug some more, and pulled the box out of the rack to hook up a VGA
card (old box w/o built-in VGA or serial-redirection), and discovered
that PCI bus-mastering was disabled for the IDE controller.  I enabled
that, as I think it's a requirement for DMA operation.

Second, Frank Smith suggested recompiling the kernel with specific
support for the IDE controller.  I chose not to do that, but it did make
me realize that I did not have the PIIX4 driver loaded (piix.o).  I'm
not sure how I was able to use the disk without that, but once I loaded
that module, DMA was enabled auto-magically.  I am now able to pull 28
MB/s from this disk in UDMA(33) mode.  Thanks for prodding my gray
matter, Frank!

Tomorrow morning's run should be the final test!

Eric