This reminds me of an old idea I called Reverse MFA where the person you're talking to over the phone must provide a valid 6 digit number before you give out personal details like birthday, SSN, etc.
In other words, phone number plus a 6-digit extension, otherwise voicemail.
Sort of like your code, but allowing a person to talk to you in the first place.
(If it isn't directly possible, I'm fairly sure using some sort of iot telephony servive would help getting hundreds of legitimate numbers. Now only to build a cell interceptor to funnel them all to one phone!)
Last I knew, they used T-Mobile for their cellular connection.
but it could be like letting smart people organize their life using email addresses in a similar way: foo+extra@gmail.com