The .303 reference got me thinking about military calibers... What would be wrong with using a good old fashioned 8mm Mauser for elk? Similar ballistics to a 30-06 with a larger bullet diameter and slightly less recoil (depending on the stock, weight of the rifle). Hornady makes a great 195 gr hunting load for it.
It may still be more recoil than she would like though. Just a thought
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