That's good information.
It sounds like a type of Reverse Captcha.
FormMail now has ATTACK_DETECTION_REVERSE_CAPTCHA which does something similar.
We use a minimum of two fields. One field has a known value - so this "proves" that it's not a random attack but one that's come via your form.
The second field must empty. So, if a bot fills it in, we know it's not a human that has filled the form.
Other fields can be included for additional strength, but it's probably not required.
But, I like your idea of generating a random value that is passed to FormMail for checking.
The question is: if a bot just left any existing non-empty text field unchanged, would that not defeat your random value technique?
If you can send me the URL for your form, I'd like to take a look at it in action and run some tests.