Sorry about not responding sooner...Thank you for the suggestion.
I do try relaxation methods while target shooting, but it all goes away while hunting, so I just time my shots between the heartbeats. The military take-up trigger allows me to anticipate the shot (a big NO-NO in conventional shooting), and I become adept at knowing each gun's release point on the second bump of the trigger cam. Trying to get them all to shoot at my preferred 2 3/4 lbs pull is not easy.
I usually notice my heart rate go up a bit (15 to 20 BPM) when I first spot a buck, but it starts going back down quickly when I tell myself, "He ain't yours yet, kid! You only ever miss when you get excited." A few deep breaths, settle my spine, settle into the harness, and get into the scope and acquire the target. A mental checklist - distance, downhill angle, windage, Where's he going?, Can I retrieve him? Downrange safe? take up, wait for the heartbeat, aim, fire.
It probably helps me shoot this way - anticipating the shot - having been an archer long before I took up gunsmithing and rifles. A video revealed that I was flinching before I released an arrow with as low as a 60 lbs bow, so I learned to keep my eyes open a long time ago.
Shooting out here in the West usually involves getting up to a high spot and glassing sectors of a hill across a gulch until one spots a deer part. Because these can be long distances, we tend to prefer to shoot fairly accurate, flat trajectory rounds like 7mm Rem, RUM or SAUM, 300 Win Mag or WSM, 300 Weatherby, (my favorite = 6.5-.284 Norma), .338 Win, etc. With a flat-shooting round in the chamber, usually aimed downhill, we just put the crosshairs above the shoulder and pull the trigger - little or no fuss about ballistics unless the shot is out of the rangefinder's (800 yard) limit. A deer usually goes down.
If I anticipate having time on the shot, I will wait a bit until I can get my heart rate down to 45 or 40 and time the shot. Shooting on or immediately after a beat is invariably a miss, and I do miss out on some shots that I take too much time delivering, but I'd rather pass on a questionable shot than wound a deer.