Not sure why changing of the wan address for your verizon router would affect anything. Actually not sure why your wan ip address should change unless you are turning your router off for more than 4 hours. Even if you do that the notifier should send the change of ip address to yoy dyn dns server and that should be propogated pretty quickly.
Are you running the dynamic dns option in the VZ router or using a manual notifier on on or more of your internal devices?