Leave a message with the manager saying you have the job offer contingent on a manager’s reference, so he/she knows your future is hanging in the balance. In case you haven’t done that already.

If that doesn’t work...

Go back to the hiring HR and tell them it’s against policy at the last employer for the manager to do this. If possible, get it in an email/writing from the previous company’s HR to forward to prove it.

This is ridiculous; it’s common policy these days.