"...getting the bullet there is one thing, accuracy is another..." Exactly. Like kombayotch says, the bullet matters a whole bunch. Especially at very long range. The bullet will go a lot farther than 2,000 yards, but hitting anything is another thing altogether.
A Remington factory 175 grain PSP bullet with the rifled sighted in at 200 will drop 44.8" at 500 yards. Only 1372 ft/lbs of energy will be left at 1879fps.
A 150 grain Accu-tip shoots 10" flatter at 500(drops 34.1"), has 1697 ft/lbs of energy at 2258fps. All Remington factory ammo bullets drop like bricks between 300 and 400 yards. Hunting bullets will do that. They're not made for very long range accuracy.
Match grade bullets on the other hand are. I'd be thinking a 162 grain Hornady A-Max or a Sierra 175 grain Matchking, using a carefully worked up handload, for 1,000 yards. Mind you, no magnum will be fun shooting targets out of a hunting rifle for any length of time.
For hunting, think 400 to 500 yards with an Accutip or its equivalent(Nosler BT, etc). Even that requires thorough knowledge of the rifle and cartridge. Plus a fair bit of experience reading the wind.
Don't even think about taking a 1,000 yard shot at any game with any bullet or cartridge. Not enough energy left for a clean kill.