Builder45,
Given that you can shoot your rifle/bullet combination well, I would like to welcome you as a plains game hunting client. You are not likely to be under-gunned. Remember the famous words: "Use enough gun!". If, however the recoil and muzzle blast of this very potent combination makes you flinch (and it is not a shame to admit being prone to flinching) I would rather like you to come hunting as my client with something in the 30-06 or .308 win class that you shoot well.
Now for 99% of all plains game animals a well placed 150 grain premium hunting grade .30 bullet at .308 win velocities will do a dandy job of quickly killing the animal.
You ask: What about the other 1%? I do not want to sound clever, but in nature there is always the exceptional! Here I refer to that one individual that is simply exceptionally clever, or hard to kill, or fast or whatever. Now the individual plains game that is just exceptionally hard to kill, be it of whatever species of plains game, will survive a well placed Swift A-frame 200grains at whatever velocity your .30/378WM will push it, for long enough to make for some difficult tracking. Your combination may be good for 99.9% of all individuals.
But there is still the 0.1% of the really top-tough individuals which will not only survive a well placed shot from your .30/378WM, but some will do so even with a well-placed shot from a .460 Weatherby Magnum firing a premium grade soft point bullet for long enough to require some serious tracking before finding the animal.
Just plan on bringing any rifle that you can shoot well, .308 win to your .30/378WM, shoot straight I and my trackers will take care of the rest.
In good hunting,
Andrew McLaren