I shoot southpaw and hunt deer
The .357 is at the low end of what people use to hunt deer with and so is the 5.56 X 45. A .44 mag, 454 Casull, 30 30, or other more powerful levergun would be better suited for that task.
I used right handed bolt guns years ago and now wouldn't own one for any reason. In Oregon where I hunt the ranges animals are taken vary from long spitting distance to as far as you're willing to shoot. I prefer short handy rifles that are accurate and flat shooting enough for long ranges.
Used Rem 700 lefties can be found under $400 from time to time in .270, 3006, etc and often will shoot under 1-1/2".
If you're content to restricted rangess (under 200) then the right lever gun might suit you.
An AR is a wonderful gun to own so if you want one bad enough get a Stag lefty. I hunted with mine but never shot a deer with it.