In case anyone else is digging this up like I am...Most of the medical exams are paperless now. CityMed has information about how the "e medicals" work: https://www.citymed.co.nz/services/usa-immigration-medicals
Also, there are only providers in Auckland or Wellington. This on the consulate website, assuming it's still up-to-date. We live in Christchurch so my husband had to go to Auckland for the medical.
AUCKLAND
City Med
Ground Level, Quay West Building
8 Albert St, Auckland City, 1010
(09) 377-5525
Dr. Megan Corbett, Dr. Donna Marshall, Dr. Lidia Nowak, Dr. Lisa Searle
WELLINGTON
ANZUS Medical Assessments Ltd.
142 Lambton Quay, Level 16
Wellington Central, Wellington, 6011
Tel: (04) 282-1180
Dr. David Hingston