300-400 quartering away? Shoot! With the 6.5! Use a decent hunting bullet, I like Accubonds or something along those lines. The 140 AB has an identical sectional density to the 225 gr. 338 AB. Not the weight or momentum, but it will still penetrate and do the job.
Rhetorical question; at what point is enough gun enough gun?
I've been wildly fortunate to live right in the middle of the best elk country in the best elk state, Colorado, for 48 of my 53 years. Shot a lot of elk, and guided a few hundred clients over the past 34 years to a good pile of elk. My experience has been that virtually every shot a client took with a magnum could have been taken just as well with an old '06 or 270.
Most of the time those highly questionable quartering away can you shoot through him end to end shots presented themselves they were gone before a decision could be made, and those that were hastily taken usually resulted in a miss or a wounded animal because the killer magnum was not shot accurately enough in those circumstances to be effective anyway.
A few more observations; most of the hunters I've been out with, including most of the locals, have not mastered the recoil and blast of a magnum and do not shoot as well as they would with an old standard.
Most of the old boys I grew up around, now dead and gone, shot things like the 30-30 and .300 Savage up to the '06 and 270. They were plenty adequate to kill elk and didn't kick too bad.
I've seen way to many elk shot to $H!t with magnums. I want to eat the elk, not shoot the entire front half to blood-shot hamburger!
That said I've used more magnums that standards myself, but after enough years and observations, my guns have gotten smaller and more pleasant to shoot. The .300's and larger have been replaced by 7mm and 270 magnums. Not for short to medium range killing power, but because I can still reach out to 1k with less recoil and enough power to do the job.
Okay, this was fun, but I gotta work tomorrow.
Shoot well, shoot often, shoot what you like.