I drew a cow elk tag for Wyoming and my choices are 300 Win mag with 200 grain Speer hotcor's, 30-06 using 180 grain Speer Mag tips, 308 pushing 180 grain Hornady spire points, 270 / 150 grain Speer HC or if it gets finised in time a 376 Steyr with 270 grain spire points. I give no particular order except I want to use the Steyr as it's a new toy.
The .300 Win Mag would be my first choice of those you listed, but I would not use the Speer Hot-Cor in either the .300 or the .270.
Instead I would choose a bullet that will hold together better at .300 velocities - the Speer Grand Slam or Nosler Partition at a minimum.
If you want a pointed bullet get the Swift Scirocco, Nosler Accubond or Hornady Interbond, bu I have doubts that these are better than the Partition and my not be as good - the Partition has the cross-member to limit expansion, the others sometimes expand down to their base.
My first choice would be one of the following: Swift A-Frame, Speer Trophy Bonded or North Fork bonded. I would use 180g for the .300 and 150g for the .270.