Q: changed Apple ID but icloud still asks me to sign in with old ID

I changed the Apple IDs for both of my boys iTunes accounts and have since replaced their old phones.

However, each of their phones is asking me to sign into iCloud using their old Apple IDs. When I try this it says the username or password is incorrect.

I try to use the iForgot password reset tool, but it says my information doesn't match (my birthday).

When I go to account management and try to change back to the old Apple ID/email address it says the ID is already in use.

I've spoke with tech support and they keep telling me to do the steps mentioned above.

Does anyone know how to fix this?