The consistent accuracy needed to take game at long ranges is unlikely to be had from a factory rifle. Assuming you want to shoot game at 1000 yards I would not attempt it with anything less than a .5 moa rifle. .5 moa at 1000 yards is very different than .5 moa at 100. Your going to need some surplus accuracy to overcome all of the things that happen at long range. A 1000yd .5 moa factory or semi custom rifle is going to be the exception, not the norm. But you can build something for probably similar costs.
I would have agreed with this statement in the past, but this seems to be changing with selected factory manufacturers that are focusing on purpose built LR rifles. Based on my own personal experiences and having acquaintance with a number of skilled owners of these rifles, it certainly doesn't appear to apply to the semi-custom Cooper and Christensen LR offerings that the OP is considering. The performance standard you describe looks to be much more the norm as opposed to the exception, and these companies will stand behind their products as reputable custom gunsmiths do. IMO.