I'm not a 1,000 yard shooter. To find that much open space here you'd have to shoot from one mountain top to another, across a lake, or down the median strip of the interstate.
A friend who's a pretty fair gunsmith, who used to build countersniper and entry weapons for LEO, got into long range shooting in a big way. I learned a bit about the subject from listening and studying the custom long range rifles he was building.
A great barrel in a suitable chambering will do you no good if the ammo isn't suited to the purpose. Bullet design being the first factor.
Low drag bullets, boat tails in particular, allow the bullet to remain supersonic all the way to the target, this avoids transonic buffering or at least minimizes its affect, and reduces affect of cross winds.
Flat base bullets may and often are, more accurate at closer ranges (600 yards or less) than a boat tail of the same weight.
On the otherhand.
The old timers of pre WW1 did some excellent long range shooting with long heavy flat based round nosed bullets that most wouldn't consider suited to the purpose these days, and at rather modest velocities barely breaking 2K fps at the muzzle.
The 168 gr .30-06 AP bullet was considered pretty darn accurate at any range. The core was boat tailed but enclosed in a copper alloy cap seated in the base so it was effectively a flat base bullet, the steel core and copper plug did make this bullet much longer for its weight than other bullets in its class.
Still low drag boat tails at jacked up velocities seem to win out. With recent interest in 1,200 yard matches these are almost manditory.
There are boat loads of suitable actions out there, if properly set up.
My friend liked to "blue print" actions. Major work done was in using a diamond coated wheel mounted in a bushing that mimicked the barrel shank, my friend used actual cut off barrel shanks from shot out barrels, to true up the locking lug seats in the receiver ring. The bolt lugs were then hand smoked and stoned for equal bearing and lapped in place. First proof round then finished up the mating of those surfaces. This seldom required removal of more than one thousandth of an inch from either surface, not enough to compromise a properly carburized layer.
There are a number of factors governing flight of the bullet, which are seldom noticed at shorter ranges.
Spin Drift is an example.
The bullet spins at very nearly the same rpm at one thousand yards as it did at the muzzle, but because velocity has now fallen off greatly the effect of spin drift increases the further out the target.
A prime example of this effect is the .30-06 fired from the 1903 Springfield.
A little understood phenomena was discovered. When the bullet left the muzzle there was a very slight but measurable jump to the left of the bore line.
Since the Springfield rifling has a right hand twist spin drift worked to off set this jump by guiding the bullet ever so gently to the right.
Bullet path and bore line converged at around 600 yards, after which spindrift guided the bullet more and more to the right of the bore line. So spin drift had only a beneficial affect up to six hundred yards.
I believe the slight jump to the left was due to less support on the right hand side of the receiver due to the clearance for ejection to the right.
This sort of flex is far more noticable with bolt actions that have rear lock up, usually cured by a front sight base off set to the left. When rear lock up and left hand twist are combined, with muzzle jump (bullet throw) and spin drift working together to send the bullet to the left of the bore line, as with the Lee Enfields, the off set of the front sight base is very noticeable.
So I'd suggest only right hand twist barrels, unless you are using a lefthand action with ejection to the left.