Are both the FZ and EK tickets 176 tickets issued by EK but on separate metal? If not, then EK would view them as two separate itineraries on two separate airlines, and they wouldn’t allow it. They’d want you to cancel both and rebook.

If they are issued on 176, effectively you’d be asking for a change with fare difference, but with EK refunding you the fare difference? Never seen EK agree to that. Commercially makes no sense for them. In this instance, your best bet would still be to cancel and rebook, if it still makes financial sense.

Perhaps there’s something I’m missing? Did you try HUACA?