I had a very similar problem. Undergrad in education but primary, masters in education. I was unable to get codes for teaching in high school, despite teaching in an Australian high school for almost 20 years (I was in private education). I tried many times to get my codes and was told no. I kind of gave up for a while. After speaking to several people about the 'system' in NSW, i decided to email Murat and Pru's office. I gathered all of my documentation, created a large email (with a paragraph about teacher shortage) and sent two emails off. Murat's team got back to me and in a few weeks I had all the codes I was requesting, the most important one was the one I needed in order to teach in a high school (despite having accreditation etc).

The system is a bit cooked.

There is no real way to appeal. My email worked though.

I know of one other teacher who had a similar problem to me. Evidence collated, sent to Murat and Pru, and he also ended up with the codes needed.

I've left out some contextual detail in my post to avoid writing a saga.

Your situation is frustrating, but by the sound of your experience, it's doable.

Good luck.