NZ won't be willing to do anything as you did not ticket through NZ.

The ticketing carrier, LH, must handle the reroute and that, in turn, must be worked out by the TA.

So, figure out your options and write them all down. Then sit down with your TA and discuss the realm of the possible. Let the TA do its thing and get back to you.

As to the feeder flight, as that implies a separate ticket, it has nothing to do with this situation. If you can cancel it for anything close to a refund, do so (after you get your reroute). If not, hope that the flight is itself cancelled or changed sufficiently for you to request a refund.