I used to be able to do this myself on AT&T with the secret codes you mentioned. When I switched to Verizon a couple years ago, I had to place a call to customer service to get this accomplished.
I just got a new phone brand with Verizon and called *611 and was finally placed with something claiming to be a real Agent. Quote "It is not possible for us to change the ring time or the number of rings on the Verizon Wireless cellular service, nor has it ever been an option."
You are mistaken about the changing of the number of rings and the amount of time before a call goes to voicemail on the Verizon Wireless service. If there is something else we can help with, we would be happy to.