I don't believe I made a mistake; that section is properly tagged as leisure=nature_reserve. The data just isn't complete, so a multipolygon can be created as you mentioned and then the leisure=nature_reserve and boundary=protected_area can be moved to that.

Hilltop Hanover Farm is already mapped as a landuse=farmyard subarea. I'm not familiar with farm tagging so I don't know if that's the usual way to do it.