Looks to me like they're doing the best they can in a very bad situation. In general terms, yes, it would be possible to base the DME arc on the ILS/DME but...
1. The arc will probably not be in exactly the same place, therefore requiring a survey; and
2. The NDB may not be well situated to provide lead-in to the arc, step-down on the arc (if necessary), and lead-off the arc onto the Localiser. But, even if it IS situated where it can be used, it would have to be surveyed.
As a procedure designer, I can tell you that it takes a long time to design such an approach procedure. Then it needs to be flight checked by suitably qualified personnel, who may not be readily available for the job. I'm guessing that ACNZ would have to do that and they have lots of other work commitments under contract so this job would have to wait.
All in all, it would be a lot of work for such a temporary outage problem. In short, the job couldn't be done - and the approach couldn't be published - in such a short timeframe. The method that has been used is clearly a stop-gap and, from where I sit, it seems like a good temporary solution.
Best of luck!