I just called VZW not fifteen minutes ago and chose option 2, to check account settings and information or ask for technical support. The automated voice said that I currently have a newly ordered phone pending activation. This is definitely a good sign, at the very least. This at least means that VZW hasn't decided to spontaneously cancel my order and that it will most likely get around to shipping within the next few days. Next I'm going to call my local store and see what extra information they can give me. ie. - tracking numbers.
If anyone is wondering whether or not their order has even gone through at all, try calling a local verizon store's number, (I don't think it will work if you call the national CS or whatever) and choose option 2 for, "If you are an existing customer and have questions regarding your bill or are in need of technical support." It should very rapidly dial another number and forward you to the national support, (I think the system detects if you've been forwarded or not). It will ask for you to enter the 10-digit number of the account that you need assistance with. Enter your phone number and it might tell you that you have a pending activation. It will ask you if you want to activate the phone now, or if you need help.
I did the above and it only worked once for me, but I haven't waited around then tried again. It only told me the message like 10min ago so it might not do it every single time that you call within a 30min window or so.