We screen our landline phone calls with the answering machine and ever since we recorded a greeting that sounds like a redirect message, we've been getting more hangups and fewer sales pitches. It appears robo-dialers that connect you to an agent can analyze speech. It doesn't matter what comes after but as long as the robo-dialer hears "The number you have reached" followed by a phone number, it hangs up. Our answering machine greeting is, in a monotone voice without audible breaths:
"The number you have reached, [our real phone number making sure all digits have the same inflection], is working just fine so leave your name and phone number after the tone. I'm going to get something to eat, OK?"
Robo-callers that deliver a message appear to either wait for the tone regardless of the wording or hang up after "The number you have reached." Friends and family will, of course, recognize your voice.
Worth a try.