I'm torn between a 270Win in a lightweight rifle like a Tikka for easy carry (especially if limited to deer), (yes, the 7mmRM would work, too)
or a 300 PRC for medium-heavy bullets, keeping velocity up to 3000fps+,
or if including elk, then maybe a 338WM or 338PRC when available, or 33Nosler.
The 338's only need a 10" twist to use the 213gnHH at 3000fps and +. The Barnes 250LRX has a .602 BC, but the 338WM would only push it at 2700fps. The 213HH at 2950fps in a 338WM would have same wind drifts out to 500 yards, literally, but would drop considerably less (-16" vs -21" at 400yards using +2" 100yd sight-in.)
The 270 and 300 would also work in 10" twist, but an 8" twist in 270 would allow the 156gnHH.