I feel the BAR in a magnum would put you easily in the 400 yard range with some good handloads and a lot of practice, no problem. And you should be able to beat that price you mentioned by a lot. I picked this one up very cheap a little while back. It's a 1970 BAR Grade II in 7mm Mag.
One more option you may want to look at, altho it will limit your range a bit is a Remmy 750 in 35 Whelen. It's a heck of a round for elk out to 350 yards if you can shoot, heh heh!
Here's three shots at 100 yards using factory Remington ammo with mine and it's a carbine. I've always prefered an auto over a bolt gun when hunting. But I agree with the others 550 plus yards is pushing it to the extreem.