Can't access AppleId for weeks, sometimes returns to normal

Question

I'm having a super annoying problem with access to my AppleID and connected services like iCloud and therefore all kind of sync jobs for iMessage, Notes and more. I'm under the impression that it is connected to my frequent travels, or/and the use of VPN. Apple refuse to help me out except to wipe my machine (which then would likely return because I need my data back up there).

I am on the most recent developer beta, though the problem has persisted across various OS X versions, beta and non-beta.

The following was either suggested I do and did not work, or I did without anyone's input:

• request 2fa code and add it to the pin/password.
• it was suggested I go visit https://appleid.apple.com/us/ and disable 2fa, however when calling that url I get an error
• double checked the hosts file weather any Apple related urls were blocked, but it doesn't look like it

Now, I'm aware I could probably access it from another device, but would like to get to the root of the problem because it's returned and gone away for the last 1.5y or so.

Is there anyone who happens to have had the same issue, or would be able to tell me what steps to take to debug this issue?

Thank you very much dear SO community.

Edit 1: changing DNS to OpenDNS servers seemed to fix it at first, now I'm back to this: