An update on my experience. After talking to the fifth agent I finally made some progress.
They would allow re-routing (2 agents would, 2 agent refused as well as one supervisor), only using NZ and LH to Europe as per original booking. Needless to say, finding Business (or any) availability on NZ out from AKL, with a connection to LH serving airport with availability, is not easy.
However I found AKL-KIX-FRA, and eliminating the stop-over and transfer through Tokyo. Although I would have preferred routing outside Japan altogether, this will suffice for now and pending changes in the current situation.
Thanks intub8r, I was about to give up on getting any ticket changes, and simply book two new Award tickets from SYD or similar routing SYD-BKK-FRA (TG) or similar, which seem to have plenty of availability, before I noticed your post.
Cheers,
Andy