WOW thats a tall order. I hope you can take a lot of time off. I also hope that you are independantly wealthy. The 270 or 30-06 would be well suited for the vast majority of the species, with the exception of the big bruins. If you have the resources to chase the dream of all 28 you can most likely afford more than one rifle, my list would be:

25-06 for pronghorn, whitetail, couse, sheepetc
300 mag either ultra or win for elk, mule deer,caribou etc.
338 win or 375H&Hfor bear, moose etc.