Unfortunately the law allows the Director to issue orders and rules as they see fit, even if they conflict with other laws. Until someone successfully challenges the director, his order remains in effect. The problem is it costs lots of money and lots of time and you're not guaranteed a positive outcome. They're using public safety as their reason, which makes challenges even more difficult.
Every incident within the parks should have been logged or generated a report. If I were challenging this, I'd start by requesting copies of activity reports involving incidents with drones. They will more than likely blow you off because it's time consuming for them to do so. So you will need a subpoena or other court order mandating they provide you the information. I would also file a complaint with the AG's office. Basically you have to disprove their assertion that drones pose a safety issue.
If you can gather several UAS operators willing to challenge this order, I think you'd be successful. The order contradicts itself. On one hand it says UAS operation is prohibited, but then it goes on to say (in the subsections) you just can't operate an UAS in conflict with the UAS Act, which is basically in an unsafe manner or in an unlawful way (peeping tom).
Good luck brother. I watched a few Youtube videos on the area and it's very beautiful, especially from above.