I recently acquired a .308 Rem Police sniper rifle with a 4-14x56 Government Model II sniper scope. I plan on using it for black bear, deer, and maybe elk this fall. Using a good quality range finder, I would like to try to kill a bear at around 500yds, a deer at 600 yds, and maybe an elk at 400-450 yds.

Since the scope is calibrated to the Federal 168 grain match cartridge, what would you guys recommend for a hunting bullet that would exhibit identical ballistics, but better performance on game as the 168gr HPBT?

Experienced opinions only please. Thanks.

BTW I have killed several elk, one bear, and dozens of mule deer (not to mention 2 cape buffalo and an elephant with 110 lb of ivory) so I am not a novice hunter.