That might be where you are better off doing the NZ conversion, you have to sit ATPL Air Law, do a medical and then arrange an ATPL flight test in the Air NZ 777 simulator. All easily organised and once you have the NZ ATPL you can use the TTMRA to get the CASA ATPL issued.
When I converted I went the CASA route and it was a bloody nightmare dealing with them. 1/2 way through the conversion I wished I had gone the NZ route.
I think you will have a very hard time getting airlines to accept the conversion argument, why would they. I know what you have is the same if not better than a CPL with exam passes but unfortunately in this day and age of non-aviation HR managers you will be excluded as soon as you say you don't have all ATPL credits.
On the other hand, why not just do all the ATPL exams and forget the conversion?