If meat has been compromised you fall into the 160 degree internal rule. If it's been marinated, temp probed from cold, tenderized or compromised in any way it should be brought to an internal of 160 degrees. That means if you stick your temp prob in a nice juicy beef roast from the get go, forget eating it rare. It has to be brought up to 160 degrees. I know the rule has changed a degree or two but I go by 160 which means I will take it to at least 155 then let it rest. If you don't compromise the meat then you don't have to reach an internal of 160. I don't worry about the 40 to 140 in 4 because I always smoke at 225 - 250 and if you leave it alone, you'll be well within that range. I use to temp probe at the beginning, but I rarely temp probe at all any more. I know when to start checking it for being done so I don't start checking the internal until almost finished. If your running your smoker 225 to 250 your gonna hit an internal in 4 hours. You have to remember... even with a larger piece of meat... it will take it a little while to even get to 40 if it's been refridgerated.
I can't really comment on the deer hang time... but if you hit it with a bullet or an arrow to kill it, you've introduced bacteria. I'll have to ask a couple hunting friends of mine about that one. A deer hanging dead for 36 hours in 70 degree weather doesn't sound appealing to me, but..... like I said. I'm not a hunter so I wouldn't know. I know I wouldn't eat a fish that had been dead that long without ice.