The biggest thing about longrange is practice. With enough practice you will learn that a 308 with the right bullet will outperform a 300 mag with the wrong bullet once you pass 350 yards. Bullet selection is critical.
That said I would look into something like a Remington Sendero, but they don't come in left hand. A Cooper rifle like the excaliber could be had with the left hand costing 200 more. To be honest shooting prone with a opposite handed bolt is pretty nice, you just need a lefty stock and a right action, although that does not make a good all around rifle.
I would think if you want a truely accurate rifle, you would be best served finding a donor action (buy a lefty rem sps or a savage, in a magnum caliber) and replace the barrel and get a decent stock. The remington trigger can be tuned nicely, despite what the tv says, and I actually like the accutrigger. Sell off the factory barrel and stock to recoup some of the cash. I did a bit of searching but there is not much in the way of a long range rifle built for a lefty.