I'd suggest fixed power, 4x or 6x.
Be a shame to mis-estimate the distance, or size of the critter, or bullet drop placement, because you thought you were on 3x of your 3-9x40 scope but really had it set to 4x.
The size of the intersection point of a fixed 4x scope's fine reticules is probably less than a half minute of angle. That shouldn't obscure the kill zone of an Elk until he's well outside your acceptable ammunition accuracy variation (with 2MOA ammo and an 8" kill zone, that's 400 yards assuming you know your trajectory). That scope crosshair only covers 2 inches of the elk's body at that distance.
Higher magnification just shows you how much your rifle is wobbling (that isn't as apparent at lower magnification) and makes you fuss your shot. Unless you are a super-shooter that can really and truly hold a rifle STILL.
IMO, anything beyond 6x magnification is for guys who can look at a target at 500 yards and not only can they hit an 8" target at that distance.... they can call out that they will hit a particular part of the target (like 12 o'clock on it, halfway up). At that distance, a half MOA reticle intersection will cover 2.5", but increasing magnification from 4x to 12x makes that intersection 1/3 the size, or just over 3/4". If you can't hold a sub-2.5" steady hold at 500 yards, it does no good (if your goal is that type of accuracy).