I too transited through IAH recently. Air NZ passengers get their own lanes at immigration, however baggage claim can take a long time. Transit bag drop off is immediately to the right after Customs, then you proceed through security (the only bottle neck I came across).
An onward journey on AC (I travelled on AC596) requires you to catch the train from terminal D to A. It's doable, but if delayed into IAH, you'll potentially cut it fine, even travelling in J.
UA also has a flight departing at a similar time to AC, with a shorter inter-terminal transfer (to C).