Congrats!!!! That thing is a MONSTER!!! Sounds like a story you'll remember for a lifetime.
I've hunted deer and elk in the Rockies as long as I can remember. Heck I was concieved on a deer hunt but let's not get off topic. I've always wondered how run and gun hunting/shooting in the high country compared to military shooting. It sounds like they can be two different animals in some cases. I spend a lot of time and energy practicing for scenarios exactly as you found yourself in. I've even passed up some shots because I couldn't get steady enough.
You probably have forgotten more about shooting than I know. With that being said I have always believed that proper breathing was important to accuracy but when I'm out of breath I have found that if you can aquire your target quickly it's helpful to hold your breath and you will actually be a bit steadier. Works for me anyway. I only hold my breath though when I'm panting heavily......it's not something I would do in a calmer situation. Has anyone else tried this?
Bring them in on a string. I love this term, if you want to be successful on calling in Elk, try not to just sound like the other caller. We all laugh at each other when we are practicing Elk calling at home or while camping. When I first started calling in Elk, I had no idea what i was doing and it's funny how many I could call in. The biggest Bull that I have called in to date was actually my first. I was making cow calls and screwing it up big time. But it's obvious I didn't screw up...