So I've just got it working again, after days of messing with it. This is what I did.
I have the luxury of a Mac Pro, with multiple drives...
1. On the El Capitan system go to System Preferences > Sharing and see what your Mac is called. I think this is important.
2. Put a fresh clean install of the Yosemite OS on one of the drives.
2. Create a test account, like Apple Support suggested I do yesterday.
3. When it asks if you want to log into iCloud Say No, and create your test login.
4. After you are totally logged in, go to System Preferences and Name the MAC the same as what it is in El Capitan.
5. Open the iMessage Application. Enter your Apple ID and Password.
5. It will of course work.
6. Logoff Messages, I did it from the Preferences menu.
7. Quit Messages
8. Boot into EL Capitan
9. Login
9. Go to sharing and make sure one last time the Name of the machine matched what you saw in the old Yosemite OS.
10. Go Start messages and you'll get the opening login screen.
11. Login, if you're as lucky as I was it will start right away, then you can go to your iPhone and set up the transfer of SMS messages too.
So why did I try all this? I looked at my iPhone this morning and saw a bunch of different machine names for rmy MacPro. When Apple had me reinstall with a test user it called my machine "test's Mac Pro" and that name is in my iPhone, along with about 5 others that I used when I kept trying reinstalls of the new OS to try to fix it. I was also a Beta tester, and had that users name in there as "Stephen's Mac Pro"
The real name of my Mac Pro has always been "KDS Mac Pro", so I don't know exactly what in this list actually fixed the problem, but I really think it's security/protection related and somehow linked with the sharing/machine name.
I'm going to reboot now to see if that breaks it again. I'll post back
Steve