Thanks, Gary, for your insightful reply.

I followed your suggestion twice (each time installing a different
version of the same driver), to no avail.

While in the Device Manager tab, I noticed the following duplicates:

Universal Serial Bus Controllers:
USB Root Hub (3)
VIA Tech 3038 PCI to USB Universal Host Controller (3)
System Devices:
Motherboard Resources (2)
ACPI IRQ Holder for PCI IRQ Steering (8 -- I think it was present
only in Safe Mode).
Network Adapters:
Dial-Up Adapter (2)
(There were only one monitor and only one display adapter in the list.)

In addition, I thought I would add the follwing notes:

- At some point I noticed that the BIOS option "PnP OS Installed" was
set to "No." I changed it to "Yes," saved the changes, and repeated
your suggestion (for the third time). As disappointing as it may sound,
it did not make any change, and the monitor yet refused to reveal its
refresh rate modes to Windows.

- At some point I also booted to Safe Mode, removed the monitor, and
restarted with a different CRT monitor (which, I know for certain, can
do better than 60 Hz) plugged in. Even this attempt failed, and Windows
did not update the list of refresh rate modes.

- It's interesting to mention that in all of the above cases, Windows
always detected the plugged monitor as "Default VGA," and not as a
"Plug & Play."

It seems it's one of those unlucky cases, but if you think anything
else can help (perhaps removal of those duplicate entries, or changes
to the BIOS), please let me know. And thanks again for your detailed
reply above.