Maybe prefix the answer with "precise match only," in all caps?
I think the "random but actually meaningful" route is better. If you want it to get checked, grandma's name comes off fake name generator, not line noise from a CSPRNG.
A CSR is much more likely to expect correct or similar words than a correct or similar string of gibberish.
Correct Horse Battery Staple
WHat's your mothers maiden name?
Correct Horse Battery Staple
What's your favourite movie?
Correct Horse Battery Staple