I see various lumber jobs in the paper. Check today's search:
Tiny URL for Trademe (not sure how long these jobs will stay in, but at least should be good for a few days)
See the ones for Nelson Pine. Now they may not be appropriate for DH but over a period of time you can glean out what the companies are and who is hiring. If you want to be proactive I would call those companies and speak to the receptionist and get a name of their HR person. I would then send a CV to that person along with very specific details of what DH does currently and any particular special skills and aptitudes he may have. I would be very open about where you are and what you are trying to accomplish and how long it would take you to pack up and move given the opportunity. If you look on these boards you will see that people with job offer tend to skate right through the INZ process. I would consider calling and following up a week or so after they've gotten the letter.
I would also send the same letter and CV to a person in a position which might need to hire DH, sorry don't know the industry but that might be the "warehouse manager" or some such title that oversees shipping/receiving functions. A lot of these people don't really want to conduct job searches, given the choice. It can be expensive and time consuming and not particularly fun. So if the papers are already on the desk for someone who has the skills... it's the old right place at the right time. It is always possible you could get a match.