I would not hesitate to take Deer with an 06 to 700 yards or maybe farther. Dave King and Ian McMurchy have taken Deer to at least 700 yards with the 308 Win. I have a 30-06 with a 26 3/4" Krieger barrel that gets 3020 FPS with 168 grain bullets and just shy of 2900 with 175, 180 grains. That is the type of purformance that a properly set up 06 can get.
Also a 6.5-284 or 6.5-06 are both excelent options as well as is the 280 AI. The 280 AI will nearly equal the 7mm Rem mag in performance. Many options to choose from.
range it,check the wind, dial in correction, aim and only one shot