Reaming out to the Ackley Improved version will probably get you 100 fps +/-. I have an '06AI with a 25" barrel and it will do 2950 fps with a 180 gr bullet.
The 300 Ultramag will do 3200 fps with the 200 gr Nosler Accubond in a 26" barrel and that bullet has a BC of .588. It will lay the smackdown on any of the species you listed out to your max yardage, but it does have fairly brisk recoil. A muzzle brake
would tame the recoil but hearing protection must be worn at all times when shooting with some of the more effective brakes. The 300 and 338 Win mags would also be very good choices. The 200 gr Accubond can be launched at around 2950 fps with the 300 WM and the 225 gr Accubond with BC .550 can be launched around 2850-2900 fps by the 338 WM.