Just got home from Kakadu. There's $25 per adult permit that you're supposed to buy to access the park.
We were coming into to Kakadu from the southern end, so the first place to get one was at the roadhouse near the entrance to the park- nope, they no longer sell them, get one at Cooinda was their advice.
4 nights of camping later we arrive in Cooinda, sorry, we've sold out, try when you get to Jabiru.
3 nights of camping later we arrive at Jabiru, office closed, come back tomorrow. Next day we had a full itinerary and didn't make it back in time.
So after 9 days of visiting the park, and 3 attempts to purchase a permit, and 1 day left in Kakadu, we gave it up as a bad joke. We had the intent, but there was no capacity to purchase.