Sorry, I haven't been on here in some time, but just as an update: We did finally get approved, but it was a headache. I ultimately had to personally email the Australian Federal Police and get them to confirm in writing that we had the right type of police check. They had recently made slight changes to the form that the NVC was not aware of, which is why it kept getting rejected. I also emailed the US Consulate a copy of the police check and they also said in writing that that was the one they were looking for.
I then submitted the new police check along with corroborating documents from the AFP and US Consulate (I literally made PDFs of the emails and highlighted the parts where they said it was right) confirming that we did in fact have the right one. Our documents were sent for a supervisor review, and at first it said rejected again but in actuality it was just being reviewed. Once a supervisor actually looked and saw we were right, it was finally approved. We also then applied for an expedite request citing financial hardship (my husband was stuck in Australia and couldn't really start a new job while await an outcome on his immigration status), and we also cited administrative delay and pointed out that we'd had to submit the paperwork 3 times even though it had been correct the entire time. We were approved for an expedited interview and my husband got his interview appointment date within a few days. From there, it was smooth sailing but I will never forgive the NVC for making this process unnecessarily painful over a single form. It appears that, almost a year later, they still haven't address this problem.
Gray & Hockey got a reaction from Redro in National Police Check Rejected (Second Time!)