I think anytime you aren't killing the first legal animal you see, you're hunting for more reasons than just meat.
I'm not convinced that when we don't shoot the first animal we legally can that it just automatically falls into the category of trophy hunting either.
I'm also not convinced in any way, that whatever definition we give trophy hunting that its "conservation" either.
Continually selecting animals with the largest antlers/horns is not conservation. True conservation would be killing animals across the spectrum of the population. In nature, the youngest age classes have the highest mortality. If that's what we're trying to replicate with hunting, then humans should be killing a higher percentage of younger age classes over middle aged and older age classes.
The same to a lesser degree with the older age classes, mortality in the old age classes have more to do with weather events than predation. Also, a segment of the populations should die of old age, that means we're providing everything that species needs to live a full life.
Yet, human hunters rarely select the young of the year, and there just aren't many animals that reach the older age classes, so hunters aren't selecting those either.
What we all tend to select are the least likely of the species to either die from predation OR from weather events, in other words, I don't know that we should be trying to sell the public on "trophy hunting is conservation". I don't believe it is, at all. We are NOT in any way replicating what happens with natural selection (including what happened historically when people did hunt for survival). We have the luxury of hunting for all kinds or reasons, reasons that our ancestors didn't get to enjoy.
IMO, its best to just say that we all hunt for our own reasons, and we all kill animals based on our idea of a self imposed selection process that likely differs from hunter to hunter. And that's good enough, and really doesn't need to be defended.
What we can all agree on is that we want to have deer, elk, pronghorn, moose, goats, ducks, fish, and even those animals we don't run hooks or bullets through, to be around in high enough numbers to keep the populations viable.