Honestly the .270 is about a perfect cartridge for your situation. The bullets buck the wind well and it is a very flat shooting cartridge with 130 grain bullets.

The .308 is an excelent cartridge but it is the little brother to the 30-06. The case measurements are identicle to the 30-06 except that it is shorter. Therefore it holds less powder and starts out slower than the 30-06.

As far as the 7mm Rem mag goes it isn't going to shoot any flatter than the .270 does out to any practical hunting distance of less than 400 yards. As factory loaded the 7mm mag firing a 140 grain bullets is only about 50 fps faster at the muzle than a .270 firing a 130 grain bullet.

AS far as needing more power for something bigger than deer you don't. The .270 is certainly up to the task of larger than deer animals. It's all in where the bullet hits the animal assuming the bullet you are using is designed for the animal you are hunting.