243, 308 or 338 Federal all sound good to me. If staying with 243, I would switch to a premium hunting bullet to maximize it's effectiveness. The premium bullet would be better in most rounds.
A 308 AR10, might give her reduced size and recoil do to its MSR shape, gas system and muzzle device.
If you went to an elk rifle, something like 338 Federal or 35 Remington with a nice recoil pad, muzzle brake and possible a mercury recoil reducer might really tame the gun for her.