I don't have the 70-200 GM II but tried it out at B&H and fell in love. It's relatively light and the image it produced was gorgeous. My one hesitation, and to your point, it might be too long for landscape and too short for wildlife.
The first lens I bought for the Sony was the 24-70 and then picked up the 200-600 which stays on the camera about 80% of the time. I'd love to fill the gap with the 70-200 f2.8 but I'm completely happy with the lenses I currently have. That 2.8 still talks to me though.
Elder Scrolls Online, by far