I found out that while Dell shipped OptiPlex 780s with "PC Speaker optional" (and mine doesn't have it), a beeper remained standard issue to issue diagnostic beep codes at boost.
This
helpful site
offered a number of ways to sound the beeper and speaker, and I verified that I can make the beeper work with:
for i in {1..1000000}; do echo $i; sudo sh -c "echo -e '\a' > /dev/console"; sleep 2; done
At the moment, it can't be heard over the machine while it's cutting, but if it still can't be heard over the machine at-idle, I'll see if I can upgrade the 12-yr-old machine with a speaker. (The baeldung site referenced even has code to play tunes on the speaker! DA-da-da-DA-da-DA!)