Hello Matt85 and other Long Shooters,
Seems to me that, with regular long range practice, you will be able to hit game, (large vermine such as baboons/jackals as well), out to at least 400M/yds, with your "regular" .338Wnchstr, provided your PH is Announcing the distance, via his laser range finder.
I suspect as dedicated as you are, even 500m/yds, probably more is in your future, with no super special fancy cartridges or gadget-rich scopes.
My first rifle (at age 16) was a 1903-A3, Smith Corona .30-06 Springfield, unaltered in any way.
With issue "peep and blade" sights, I shot many ground squirrels out to about 200 yds and more than one or two stationary jack rabbits, out to around 300 or perhaps more.
Couldn't see these rodents very well, beyond those two approximate distances with no scope.
Since those times, I graduated to a 220 Swift and old Leupold 10x scope, with fine cross wires and "target dot".
With this simple outfit, I regularly shot ground squirrels out to 400 yds, using almond and/or walnut tree spacing by counting them, in orchards as "range finders."
Many years later, during my first African trip (Namibia), I brought a .300 H&H Mauser / 180 gr Nosler Partitions at something over 2800 fps.
It was equipped with "only" a Zeiss 4x scope, with standard cross wires, mounted low, in older Talley lever rings.
Shooting over sticks with that simple rifle and 4x scope, I had no trouble shooting very dead, at least one gemsbok and one springbok, at a little over 400M each, according to the PH's Leica range finder.
I now cannot remember if there was another 400+ meter/yard shot from myself during that trip or not.
But I do not think so.
Likewise, I once owned a plain old Remington 700 ADL in 7mm magnum.
It liked 150 grain spitzers, at a bit over 3,000 fps.
I bought it used, with a 4x Leupold, in Redfield rings/one piece base on it and eventually I switched to a Leupold 6x with duplex reticule.
In those days, Civilian Cops were allowed to use the Army Rifle Range, once in awhile under certain terms.
For this, I zeroed my scope straight on at 200 yds.
And discovered I could hit the 500 yd steel "lollipops", by using the pointy end of the lower duplex (that tapers upward, to produce the smaller vertical wire or "hair"), by holding the point at "6 o'clock on the target.
I believe theses targets were 16" but, perhaps they were slightly larger or smaller, not positively sure any more.
This 500 yd "gong shooting" was from prone, over my day pack as a sturdy rest.
It was very satisfying to feel the recoil, and hear the "bang smack" and upon regaining my sight picture, watch the "lollipop" swing back up into view for another smack down.
Anyway, my point is that you are an above rifle shot and so, if I could manage the above shots, in my 40s and 50s back then, a young, sharp eyed chap like yourself should have no problem hitting the mark, out to at least 4 or 500, from prone with light spitzers at around 3,000 fps, from your .338, not to mention your powerful scope.
Cheers,
Velo Dog.