This problem has been solved a long time ago by the Departments of Fish and Wildlife for hunting and fishing. A lottery that is tied to an identity, no transfer allowed. Psuedo-RNG, so that each time you enter the lottery and are not selected, your chance to be selected increases next time. The money from the lotteries are used to help conserve the resource that they draw on. Example: https://idfg.idaho.gov/press/bighorn-sheep-lottery-tag-raise...

This is not a new or unique problem, and hunters and fishers figured out the solution a long time ago. This could easily be applied to local, state, and national parks. Well, easily is perhaps not the correct word, but there is a known solution to the problem that _can_ be implemented.

EDIT: Hunters and fishers figured this out because they fucked up big time and nearly eradicated large populations of animals (see Bison). They (or the D of F & W's) realized they had to do things differently if they wanted to sustainably continue to hunt && fish.