Please don't take this as possible criticism, as that is NOT how it's intended...
If this was your first elk hunt, it might be a little early in the process to start thinking about taking shots on a moving target through the woods. Very typical to have a bunch of elk moving at once, which makes picking and staying on your intended target in the trees pretty challenging. And you heard multiple shots while you were hunting...there is always a chance another hunter could be on the same group of elk from a different direction.
Could be that I'm just overly cautious, I have tried to avoid moving shots at big game whenever possible, and doubt I would venture to take a moving shot in the woods. Other people's methods may vary, and that's fine. Best of luck out there.