I disagree with one aspect of your statement.
Hunters can be conservationists too. I work in biosecurity, have worked for DoC for a few years as well, and regularly volunteer trapping in the Northern Ruahines and Kawekas. To draw a line in the sand saying you’re a hunter not a conservationist ignores a lot of nuance around why people do the things they do. Some guys shoot whatever they see, others shoot bugger all. But the net effect is on the whole, positive for biodiversity. But only in the fact that a deer is dead.
But I may also be misinterpreting your statement as well.
Determining carrying capacity of an area requires informed data specific to local ecosystem type and maybe indeed by catchment. Figure out the numbers of deer currently in there the best way you can and then aim for having a lower density herd. @
Gibo is right in saying that they need to be managed as a resource, but who pays and who says.