There is good news and bad news here....
The bad news is that your options are relatively limited, especially once you get above the .375. The good news is that especially on the used gun market you can find some deals if you look hard enough. There just aren't many lefties looking for a .458 Lott!!!
Current production CZ makes a left hand .375 H&H. I have one and love it. They do charge I think about $600 more than the right hand version.
I think Ruger also makes a .375 Ruger in left hand, but ammo is limited unless you handload. The most options you'll get are from Montana Rifle. Jeff is a lefty himself and he has options and its a good solid rifle. You'll read some poor reviews on them, but you will on CA as well. For ANY off the shelf rifle I would always buy it at least a year before I needed it if at all possible. That will give you time to get it right or switch gears if need be.
I was going to buy a Montana until I found a used Brockman in .458 Lott (Montana action ironically), with which I've been happy.
The last thing to keep your eye out for is a Winchester Model 70 left hand. They don't make them anymore but they did and I's love to have one. You won't run into one very often....
Hope this helps! Let me know if you have anymore specific questions. I shot right hand bolt my entire life, but after getting used to left hand I only buy those now. they are there, but like I said you have to do some looking.