Money is cheap, it's time that's expensive... I don't have any experience here, but my intuition is that organizing and executing the event with appropriate bureaucratic signoff, managing PR, reviewing all the candidates (in a fair and unbiased manner), etc... sounds like weeks of effort spanning months, no?
Philanthropically, people do this scale of stuff for their own communities all the time. In the arts, people stand up and run themed contests every day.
There is absolutely time to be invested in designing or approving whatever online presence, reviewing submissions, becoming comfortable with whatever legal requirements, etc — but that’s the part that makes it a memorable life experience, not unlike the time spent on that trip to Belize or in those woodshop classes.
How interested are you? If you or someone you know can provide the money, I bet I can find someone in the parks service, or a close connection, to handle the bureaucratic side of it. (I was an environmental science undergrad, and we frequently worked with the NPS and similar entities. Culturally it's very different from the tech world; they are often budget-starved for things but can make time for events and such.)