I'm not saying there are not people capable of the shot, but the hype and BS surrounding taking an animal that size at 1000 yards and dropping it in it's tracks is just that BS. The editing of those shows is done strategically and is misleading. There are factors at play at those distances that 99.9 % of hunters know nothing about. As you stated wind currents and thermals are a complete unknown in the areas where these animals are hunted. Your not pulling up an AP on your phone for it. Go out west or on the plains and hunt, one out of every 30 days you may have calm winds. Long range target shooting and killing animals of that size with one shot and dropping them in there tracks are two completely different things.
I see where you are coming from as far as the editing etc. I don't think that the average Joe is going to make those shots either, but the guys on those shows are not average joes. I know guides who frequently have patrons who make 700 yard shots. They ask them if they have ever made a shot like that, and often times will have the patron use the guide rifle, because it is proven, and he knows the dope by heart.
In the case of the op, it would still seem to me he needs to spend some time putting rounds down range until he can produce respectable groups @100 if he wants to shoot at range. 3-500 is the beginning of medium range. Any modern high power rifle caliber should be able to make 500 with realative ease. When you start stretching past 500 is where things start to get more complicated.