I'll help you out here.
Google Voice.
http://voice.google.com
If voicemail isn't good enough let it ring to your cell number then after the verification turn off the redirection to your cell. Your real number will never end up in Whois then.
BTW, I think the verification is BS as well. Godaddy called me a few days ago and left some automated thing on my VM. The problem is everything was cut off except for "Thank you for being a GoDaddy customer, please call blah blah for more options." If I find this was some sort of verification I will be pissed since my number is legit (Google Voice). If they are allowed to pull domains for this there should be clear procedures and limits to it. They shouldn't be able to pull your domain in a couple days because the automated tool thinks you used a false number. I'm not about to go through voice menu hell with GoDaddy each time their stupid machine leaves an improper message on my voicemail. That's ridiculous.
Btw, I do not recommend GoDaddy. I used them recently to get a $1 domain and I have some old domains which would simply be too much of a PITA for me to transfer because they make it so difficult with their BS.