Even though your skills, experience and occupation may be on the LTSSL it doesn't mean it'll be easy to get a job in that occupation. It all depends whether or not there are enough skilled people already in NZ with the right to work or not.
A tiny number of the occupations off the LTSSL will have a serious shortage of the skills and experience in NZ and the employers looking for the people with those skills and experience will me desperate and will be looking overseas.
If you fall in to one of those occupation then you are in with a chance. If you aren't then it's going to be very difficult to land a job here while still overseas.
Many employers are only interested in people who are in nz and have the right to work. They do not want to have to wait for overseas staff to appear. They don't want to get involved with Immigration issues. They don't want any extra costs or time constraints. Many probably steer clear of overseas applicants so they don't have to offer or pay out a relocation package. Many employers want overseas candidates to make some commitment to nz before they will show any interest.
All you can do is to keep applying. Try to point out to employers in your cover letter that you will have more chance of a visa if you have a job offer. Put their minds at rest that you are already involved with Immigration and will do all the work necessary to start work quickly even if that means applying for a temporary work visa (essential skills visa) so you can travel over more quickly. You can do this and have the Resident visa application ticking along in the background.