Can't Re-Associate my iMac to Apple ID

Hi, and sorry – it's a long one.

I can no longer sign into iCloud or iMessage / FaceTime via iMac (OS X 10.11.6). The problem began with just iMessage, but has escalated to the point that I can no access my Apple.ID or iCloud from the iMac.

I do not have this problem on either iPhone 6 or MacBook Pro (OS X 10.11.6).

So far, I've tried the following:

Non-Invasive

⁃ Checked OSX 10.11.6 is fully updated.

⁃

⁃ Signing in from Safe Boot.

⁃

⁃ NVRAM and SMC reset.

⁃

⁃ On/Off switching of Location, Date & Time, and Firewall.

⁃

⁃ Various resets of Apple ID passwords and security questions.

⁃

⁃ First Aid from Recovery Mode. Exit Code 0, squeaky clean).

⁃

⁃ Signing in from a newly created secondary Admin account on the same partition.

Invasive:

Signing in from a repartitioned drive.

Deletion from ~/Library/Preferences of the following plists:

• com.apple.ichat
• com.apple.icloud
• com.apple.ids.service
• com.apple.ids
• com.apple.identityserviced
• com.apple.imfoundation
• com.apple.imessage
• com.apple.imservice
• com.apple.madrid
• com.apple.imessage.bag
• com.apple.imagent.plist
• com.apple.security

Removal of revoked certificates and deletion from Keychain of entries related to:

• IDS(user)Auth-Tokens

• ids:message-protection

• iMessage

• iMessage-protection.

From Terminal:

• killall identityserviced

• killall imagent

• killall securityd

• killall securityd_service

Ultra-invasive:

⁃ 3 litres of strong coffee and a half a bottle of Jack Daniels.

I then disassociated the iMac from my Apple ID, thinking I could simply add it back again and (perhaps) the problem would disappear. Who was I kidding? A whole new world of pain opened. Now I can't even log onto iCloud (so no Mail now, either).

Before I'm asked: I can't reinstall OS X from Recovery Mode since I can no longer log in to my account via the iMac.

I do have a couple of copies of the OSX 10.11.6 image which I copied from the original download by aborting the install and locating the image file. But before using that, I'd need to be sure it's not going to compromise any PACE, iLok, or licence signings. It's my studio machine. Besides, I don't think it will solve anything since this seems to be an Apple issue, not an OS X problem (no problem on the MacBook, iMac functions perfectly apart from iClutter).

At some point in the chain it seems my iMac has been blocked/compromised by Apple. As stated, I have full functionality with the MacBook and iPhone.

Apple Support is giving me the traditional run-around, so hoping for some help here – maybe the Linc Davis co-operative is listening in ,-)

Any ideas?

Anyone want to buy an iMac? I'm going back to pen and paper.