Hi Darren,
If you are certain that you are trying to sign in to iCloud and Messages with the SAME Apple ID and you are getting that error then I would recommend that you contact Apple Support. You already did that and it appears that Apple has not fixed the issue for you. I am afraid that if Apple has not been able to fix this then the folks here may have a difficult time with this as well.
Below is what I recommend and pardon me if you have already tried the solutions offered-
- Open Settings ➔ Apple ID (Your Name up top) ➔ Sign Out (at the very bottom
- Open Settings ➔ Messages ➔ Send & Receive ➔ Tap on your Apple ID and Sign out. (You may not be signed in here and that is fine).
- Force ReStart Your iPhone exactly as shown in that link
- Repeat steps 1 and 2 however this time SIGN IN with your Apple ID and ensure that the Apple ID credentials used are the SAME for both (Messages and iCloud).
- Open Settings ➔ Apple ID (Your Name up top) ➔ iCloud ➔ Messages Set it to ON.
If the above does NOT work then I recommend that you ➔ Restore Your iPhone to Factory Settings and begin setting it up from scratch.
Axel F.