.338 LM, .408 Chey-tac, or .416 Barrett are my serious contenders. .50 is out as it just isn't accurate enough.
Looking at either a Vigilance VR-1 as an "off the shelf" rifle. Or possibly customizing one with a Surgeon 1581 XL actions as it's base. Possible Kreiger barrel. I'd custom build a stock for my left-handed shooting style.
.338 LM has broad availability and good accuracy, even on the far end of it's envelope.
.408 Chey-tac has better range, similar accuracy, but the brass and bullets are as rare as Hen's teeth and the company may be having internal troubles.
.416 Barrett, brass is expensive, range is exemplary, but finding an action/barrel chambered for it is difficult.
Precisely what is holding me back. It's expensive enough to handload the .338LM, I paid $2.50/casing (Lapua) from Midway a couple of months ago, with the price of the other components initially approaches $5/round. I have reloaded 20 cases 5 times each. Good thing I can re-use the brass a few times, and I've got 80 cases I haven't even touched yet.
.416 cases run upwards of $4 ea (unprimed) last I checked.
Go with the .50 BMG. Ammo will be far more available for that in the coming days than any of the other platforms you are considering.