Hi, everyone.
I haven't been watching this thread for a while, so I don't know really where we're at, but I thought I'd share my story with you and maybe it'll help someone out.
First off, I've had an Apple ID for a few years now, and when I got my hackintosh built, I wasn't careful and got by ID blacklisted by Apple for logging into iCloud / iMessage several times with different SMBIOS configurations. I realized my mistake and made a new Apple ID. I followed this guide along with several others to a T, and I kept getting the call customer support message.
Through the course of several calls, it became apparent that customer support simply could not help. They entered the error code into their system telling me each time that everything seemed to now be working on their end. Anything further would require an engineer to get on the case which I wasn't interested in doing because it would be revealed I was on non-mac hardware.
As such, I gave it a few months and then called Apple to report that my initial Apple ID wasn't working. It took their engineers about 4 weeks, and they finally got it working again.
So, now knowing what I was doing after doing my research, I used this old Apple ID and got both iMessage and Facetime working perfectly.
Like I said, I don't know where we're at in terms of progress with this particular issue, but if you're getting the "call customer support with error code" message, nothing worked for me. Absolutely nothing. Doing everything the same way with my old Apple ID worked easily and quickly when I knew what I was doing.
Thanks for all your help.