When my daughter started hunting, I went with a 7/08 for deer and elk. 15 years later and she's still using the same rifle. I thought the difference in recoil was negligible, as did she at the time. She was a little thing too. Different people's recoil tolerances are different; but, it might be worth a thought. I'm not trying to talk you out of the 243 as I'm a fan. In my opinion, the 7/08 is more versatile when elk are thrown in to the mix. It may open up your options for available rifles.
Another thought on your question to "just suck it up" and buy the blued 243, stocks are not expensive and I would think it would be easy to cut the stock to fit her better, if needed, and then buy another as she grows.
Not to sound obtuse Hiaring8; but, is barrel twist availability your biggest concern with what you have in mind to put together for her?
