Unable to set up a new Apple account for a family member

Despite all of frustration, it actually worked. I was able to finally create an account with that phone number. Here's how it was resolved in my case at least.

1) I Called tech support and eventually reached a senior advisor.

2) Have them "allow" or "whitelist" the phone number.

3) Wait 24 hours for the system to reset.

I'm not sure if any level of support staff can "allow" the phone number but that seems to have worked. No it was not my IP that was rejected. No I didn't need to walk away from my building and try in on my cell phone carrier. No, I didn't need to set up alternate accounts or any of the dozens of suggestions I was given.

I still hate apple, but maybe a bit less. After all, I started with a Mac Quadra running an Avid so I must have some reason for still using them for my creative work. But the draconian.... never mind.