Hunted Namibia last year, took my Eland with a 300 Mag shooting the Woodleigh 200 grain PP.
I'm sure they've been shot with smaller but I felt way under gunned. Next time I have an Eland in the sights it'll be with a 9.3x62.
The 340 will do the job, there's guys on this forum that have far much more experience than I do, that say so.
The key issue for me is what happens if you loose your ammo?
You'll find 9.3x62 and 375H&H ammo you might even find 338 Win Mag. Not real confident about 340 Weatherby.
And if you think it can't happen to you, it happened to all three of us! Fortunately we got the bags and guns back after a few days but....