This shouldn't be hard, but ultimately is.
I only found references that I should backup the existing MySite and move it to another location. The MSDN documentation on Configure My Sites in SharePoint Server 2013 is pretty thin on changing the URL.
The only viable information I found so far is:
UserProfileManager.MySiteHostUrl (gets or sets the URL for the current context). Under User Profile Administration > Setup My Sites I am also supposed to be able to change the My Site URL.
The problem is that none of these changes are persistent. I change the
MySitehostUrl with PowerShell - the change is not persisted. I change the URL via CA, click OK, the URL is gone.
I initially set up MySites to not use HTTPS, I want to change that now. AAM is set up and HTTPS works perfectly, only the URL is still wrong.
How to change the MySite Url from: