Correct an Apple ID Child account birthday to a teen account?
After much time, I now understand more about the changing of a birthdate on a child Apple ID account.
In my region (US and UK) there are bands which define child, teen, and adult. They are....

1-12 Child
13-17 Teen
18+ Adult

Basically, you can't change a birthday from one band to another. Once a child, always a child, until the system thinks the birthday rolls into the next band.
So, once a child account is associated with a birthday under 13, it can not be changed outside the band of 0-12. But can be changed to 12 years, 364 days backwards from today.
So here is the fix: Change the birthday to today - 13 years + 1 day.
Example
Today is August 10th, 2019, so you would use August 11, 2006. Then, the next day the account will &quot;naturally&quot; roll over to 13, and at that point you can change the birthday to anything in the teen band of 13-18.
I did have to also use the parental approval to approve the birthday change. So my steps were ...

log into child account, change birthday.
Log out of https://appleid.apple.com
The change sends an email w/confirmation link to parent(me)
click email link to confirm birthday change
log into parent account and confirm change.

Mission Accomplished