I think you hit the nail on the head. .243 through the boiler room will kill a critter a helluva lot faster then a .338WM through the guts.I'll bet that you would not notice a difference in recoil, between the win mag and the weatherby. If you are recoil shy, then neither is a good option. Get something less and learn to shoot it with competent bullets and your quest is over-especially only shooting to 300 yards. At that range, it is hard to beat a .308, Creed, -06, .270 etc., etc. There is nothing special about a big magnum, if you are just going to shoot moderate distances anyway. Just because it has the word "magnum", it does not kill anything any deader-except for your shoulder and your wallet.
There's plenty of ways to reduce recoil and plenty of ways to get used to it. Just shooting to get comfortable with it is the best thing you can do. The 30-06 is one of the most underrated calibers in my opinion. It's another very versatile rifle! Having a custom gun builder put together a rifle ensures the best fit for you and no matter how big of a caliber it is if it fits right, the recoil is manageable.My one rifle for all western hunting is a 90's vintage Ruger M77 mkii in 30/06. A 300 is a fine choice and any of the platforms you've chosen are solid. It comes down to fit & aesthetics. If I were buying a plastic stocked gun, I'd be looking at the Browning Hells Canyon, or a Montana Rifle Company action and a custom maker to put it together.
As for recoil, you'll only notice it on the bench. Buy a PAST recoil shield & go shoot.
All of my bolt guns except the Ruger are right handed. Never stopped me from killing anything. The biggest benefit I've found to having a left handed bolt rifle is having the safety on the correct side fo hiking, still hunting, etc. My guns don't snick off safe now. I can't use the fancy scope covers because of the left handed bolt lift, but the safety issue and having a faster recovery for clambering a fresh round more than make up for it.
I have some of each and have no issue with either one. I prefer the left-hand rifles, but I recently just added a couple rifles that are right-hand. I traded for a .270 and I bought a Remington 700, .243 that was too good of a deal to pass up. It is now wearing a 6.5 Creed barrel.
I have a number of left handed bolt actions. Three are Winchester Model 70s but you are likely going to have to limit yourself to used ones as they stopped making them (although I did see a new 7mm-WSM somewhere online the other day). I also have a few Savages and my 7mm-08 Weather Warrior is one of the most accurate rifles and probably the least expensive. I just purchased a Christensen Arms Ridgeline in 6.5 Creedmore a few months ago and it served me well with the elk I got last week in CO. If you don't want to spend $2,000 for a Ridgeline, I'd look at the Mesa. I think you will be limited to 6.5 Creed, 7mm-08 and 308 with Christensen Arms, but IMO, they will all do the trick.
I think they stopped making the left handed Model 70s when they closed the New Haven, CT facility (which I think was around 2006 or 2007). Prior to that I believe they made them for many years. I have a 300 WM, 375 H&H and a 7mm WSM (unfired and soon to be listed on Gun Broker).Not doubting you Just curious, when then Winchester ever make a left handed bolt action rifle. As far as i know they still refuse to make a left handed bolt action