I have already manufactured 60Hz transformers (not ferrite) and I think there is a mistake in principle.
As the project is not done by the manufacturer, how can it be made accountable for the value of the primary inductance of the windings?
It should be asked a dozen prototypes without imposing the inductance, check if the value of the primary inductance resulting from the detailed manufacturing specifications is consistent with what is expected and only after that, specify the value of the primary inductance and the tolerance acceptable on this value.
The manufacturer is not responsible for any errors in the client's project