Several AGM Tiapan models fall within your budget and IMO have been the leader for a number years. I would go for the highest resolution models with zoom… to not only maximize your detection range, but the identification range as well. Since you have zero depth of field, it may appear you are looking at two animals that are the same size and next each other when actually you are looking at a yearling at 100yds and a mature animal at 300.
Elk and deer antlers are clearly visible while while in velvet, they glow brightly. However, after they go to hard horn they all look like does.
Im using the 640 res Pulsar XG 35 which is a little over your budget. I've not checked it on elk but it's easy to discern cattle at extremely long ranges. But coyotes and fawns can be hard to distinguish at relatively short distances. Pixel count is more important than optical zoom…384 is the minimum.
Over the past two years I've carried it on 7 late summer Deer Night Surveys. On multiple occasions I was able to determine the sex of whitetails out to 300yds in brush when white spot light operators were unable to tell.
