To my limited understanding & way of thinking, the .243 is about perfect for pronghorns, a .25 cal like .25-06 is a bit strong, but good for long shots, and .270 is nearly overkill, but perhaps at the upper end not being "overkill". But like Art said, there isn't really 'too much', except for the fact that the high speed bullet makes a lot of meat bloodshot if you hit one of the shoulders on the way in or the way out.
I will say that a light little pill such as the 140 grainer in a .300 maggie would definitely get there FAST, extending your PBR to close to 275 or more yards, depending on how much margin of error you are willing to accept. And it would have almost no wind drift. So if you are shooting at ranges beyond 150 or 200 in windy conditions, then I'd say that the cartridge in question is NOT too much. Making the hit is what's important, and speed helps kick the wind's rearend. Just try to shoot broadside, not quartering away or toward, so that you get a clean ribcage entrance & exit.
The .270 WSM is arguably the ultimate LARGE game, VERY LONG range cartridge (elk, moose, and such). It's a bit much for little old pronghorns though. The main concern other than bloodshot meat is of course recoil (flinch development), and noise/blast. To a lesser extent, ammo cost.