Lets address some things left unsaid.
You're hunting? Why is the rifle slung on your shoulder as if on parade? I've jumped more deer going into my stand or blind than I care to count over 40 years. I no longer stroll to that location unless it's pitch black in the morning, I still hunt to it, three careful steps and wait at least 30 seconds slowly scanning.
You have to see a deer to shoot it, and a flagging whitetail is usually a fail in tactics.
As for Hunter Safety saying cup your hand around the trigger, not with the AR15. And with 22 years training USAR it's drilled in to keep it at a low port. I can shield the trigger with the extended finger while keeping my thumb on the safety.
When moving across terrain with another hunting buddy I let them go ahead 35-50 yards, which reduces the muzzling that absolutely will happen in the field. Again - 22 years in small units in the field, you must learn and accept that your fellow soldiers will not ND the weapon. You are as culpable as they.
Hunter safety is important, if you are with others in the field, tho, it's no different than shotgunners working pheasant, etc. You must maintain separation, have good muzzle discipline, and keep the chit chat to a minimum. They may carry at a high port because of their game, and they tend to work in a chevron to keep the muzzling to a minimum.
They don't use slings on shotguns, do they? There is a reason for that. The Army taught me in the Infantry School to remove it going into the field. It's not that much an asset getting tangled in underbrush when trying to quietly move closer to game. It makes carrying the weapon too easy when you should have been paying attention to your surroundings. In combat that can be lethal, deer hunting it can mean the difference between a good shot or watching an opportunity lost. Slings became popular when Great White Hunters had gun bearers loaded down with drillings, stalking the elusive rare ungulate across the Serengeti.
The military uses them for parades. In the field - not so much.
Lastly, just how twitchy is your trigger? Using a two pound target trigger in the field isn't recommended, and world wide most combat field triggers have a minimum six pound pull. There Is A Reason For That - stumbling across tangled vegetation, uneven footing, fatigued, and sudden surprises means that you need a trigger you know is controlled.
There is NO loss of effective accuracy with a 6 pound trigger, what is really happening is oneupmanship - installing a race gun trigger on an off road gun. I don't often see open stack injection on a swamp buggy, a two pound target trigger that might increase accuracy .25 MOA on a good day isn't going to make or break a hunting trip when you are shooting at an 18" square center of mass moving target at 50 - 125 yards. It's just the wrong part for the wrong gun.
Get the working weight of a proper field trigger back up where it belongs, to prevent ND's in rough terrain, and we wouldn't have to worry so much about a functional safety keeping it from suddenly Going Off! like it had a mind of it's own.