There are some requirements for Edge, some of which are listed below. Did you meet all of these requirements, including 6 months of on time and in full payments???
To be eligible for Verizon Edge, your device must be eligible for an upgrade and:
"MORE Everything Plan with EDGE."
You wanted to go FROM More Everything TO Edge? As in keep the same amount of Data and just enter into a 24 month payment structure on the Note 4?
Really, the only thing I can think of preventing you since you have obviously been a customer longer than 6 months is the late/missed payment thing. Verizon doesn't take this Edge plan lightly considering they are cutting loose with a multi-hundred dollar device.