While I am certainly not going to talk you out of a .270. I absolutly love mine and it's quite the capeable rifle for North Americas game.

With saying that, and since you have a gunsmith friend helping you, you do not have to stick with only the "standard" case head dimension. You can chamber it for just about any cartridge you want as long as the case head is larger or the same size as the -06. It is a simple matter of opening up the bolt face to the proper dimension. A ten minute job on a lathe. While the .270 is an excelent cartridge it is certainly not exotic like you said you wanted.

Not that this is goint to give you anything that the 308 or 300win mag won't give you but something like the 300 H&H is readily available and somewhat exotic. Or something like an 7mm STW, 240 Weatherby, 6mm Rem.