For antelope and deer, the 257 Weatherby will work just fine for long range work. It is very flat shooting, will have enough power, and you already have it. Unless it does not shoot well, then that is a different story.
For elk, it should work to as long as you limit how far you shoot it, due to bullet energy and bullet construction.
Shot placement is critical for all of these cartridges, so that will be a limiting factor with all of them.
Ok, now onto your question. All of the mentioned calibers will work. They are all good, with some having limited sources of brass. The 7mm LRM, 28 Nosler, 7mm Dakota, 7mm STW, 7mm Rem Mag, and 7mm Weatherby Mag all will work great as antelope, deer, and elk rounds for long range shooting. Just make sure that the barrel is a 1:8" twist barrel. This is so that they can shoot the heavy bullets for the 7mm. Also check to see what the mag length is, as the STW might be a bit tight in their.
As for the 6.5mm loads, they will work fine too for antelope and deer. For elk, I would limit my range with the 6.5x284 due to energy, but it will still work good. I am not sure how well the 6.5x284 will work with the bolt face of your rifle though. That would need to be checked before I would move on that cartridge.