Killer - you should have been around 45 years ago when only Rem, Savage and Weatherby were the only ones who made production left hand rifles. Today there are a lot to choose from. Being a lefty I've owned and do own several left hand bolt action rifles. My favorite model (currently) in my gun safe is my Tikka T3 lite in 30-06. This rifle will shoot 3 shot clover leaf groups all day long. But that is pretty common for these rifles. They guarantee 3 shots within an inch at 100 yds. And the price is definitely within your range even with a quality scope. Calibers for this model range from the 22-250 up to the 338 win mag. And you won't find a slicker action - except maybe on a Sako A7.
Some manufacturers who make left hand bolt off the top of my head:
Remington, Savage, Tikka, Ruger, Browning, and I think T/C has come out with a lefty.
As another option, you can go with a single shot like a Ruger #1 or a lever action like the Browning BLR.