Late post. You do not need a 9.3x62 or a 35 Whelen for plains game. I have shot nearly 200 with the 275 WinRem (270+280/2). The 30-06 is great for plains game. I would never suggest more than a 338-06 and even then I think the 30-06 is plenty if you can shoot and if you can't then go to something even easier shooting like a 7x57.
Get a 30-06 and a 270. There is some overlap but that is a good thing. On my first trip I was getting a Pre 64 M70 ready and the trigger broke. Could not get it fixed in the remaining 10 days so I got out my mauser G33/40 280 and went. On the twelve trips since I have used a 270 mostly. It has always done the job. I gave up on the 280 cause I couldn't find ammo easily although I handload. I think it is a good idea to have a pair of similar but not identical hunting rifles.