I've been wrangling these semantics in OSM for literally decades.

There is a possible solution to address most (or perhaps even everybody's) concerns in this case.  The entirety of the property, as a "protected area" (in each of the 50 states, federal law and even OSM semantics there is such a thing, replete with databases, law and much geo data) is correctly tagged leisure=nature_reserve.  That's simply a legal fact.

That some wish to see leisure=park tagging on at least some of the areas / facilities of this area CAN be accommodated with what is often called the "front of park / back of park" concept:  those areas which are "front of park" that contain things like parking lots, amenities such as restrooms, picnic tables, sport fields / facilities, etc. CAN be tagged as a (subset of the area) leisure=park.  The "back of park" areas are NOT so tagged, and remain tagged "simply" as a leisure=nature_reserve.

This isn't always perfect, but it is a compromise solution that often works.