I'm so sorry to hear about your predicament Piebird, I know how devastating it is as our first EOI was declined and chucked back into the pool. We used a Wellington based advisor who's been terrific. When we decided we wanted to go to New Zealand we emailed around 14 advisors with our details and only two mentioned we had a chance.
We went with one of them and true to her word she took us through the whole process. I've mentioned this before and I'll mention it again, having an advisor doesn't give you an edge with the process but it can be helpful with getting all the paperwork filled and exploring your options.
If you're interested I can PM you her email address and you can get an opinion about your chances.
PS: She's also secured OH a job interview for when we get there, he's in IT too.