Boy this thread has gotten away from he op's topic. I'd bet some didn't even read his rants and then what he actually wanted. Thought about your conundrum some more and here is what ive come to. Im probaly just statimg the obvious but sometimes that helps.
Yes you could build or buy then modify a .300 blk bolt gun to match the length of pull needs of your daughter. However, at this point in the market growth in the product cycle the .300 doesn't have much choice in bolt rifle barrels other than from AAC and the long awaited Remington. If a gunsmith had a barrel blank and chamber readers for the .300 they could custom make a lightweight barrel for a Remington 700. Then find a stock and have it modified or get one of those blackhawk stocks with the ar15 adjustable carbine buttstocks that are adjustable. This might be expensive though because of the products life cycle at the moment it really hasn't peaked yet it's still in the early growth stages.
The options I see if you want her to have a rifle today that meet your requirements are as follows.
You could get a rifle used chambered in 7.62x39 then just modify the stock( or use any intermidiate caliber). However, your still in a expensive boat if you use a intermediate like a 6mm Ppc, 6.5 Grendel, or something like the 6.8 spc. However, the 6mm and 6.5g both have retarded awesome inherent accuracy. So you would have a precision caliber. The 6mm you would have to reload however.
You could build a semi auto Ar15 using lightweight parts like a plumb crazy lower( dirt cheap as well). Have the 16" ish barrel in any intermediate caliber like .300blk, 6.8spc, 6mm ppc, 25-223, 6.5g, or 7.62x39. This would cost a little bit more however in terms of barrel length it fits your criteria. As far as muzzle blast goes a simple thread on muzzle device would take care of that. As far as stock size goes the adjustable carbine stock would work very well for a growing kid. Weight is a little heavier than a bolt rifle In a featherweight, but it helps tame recoil. Finally, recoil the gas system can be adjusted with a adjustable gas block and well because it's gas operated it will reduce the recoil.
If I was you I would get a ar15 Although they are expensive and well addictive. It would possibly fit your child's needs in the whole. Also if you want to work fundamentals a cheap .22 bolt gun does that well. Then she will be prepared to use the ar no problems. Plus it's so modular like my previous post with the tc dimension. It would let your child or even you to grow with it. Start .300blk and end with a 6.5 or whatever it's just like a adult gun addicts Lego set and to prove this just look at any picture thread.
Hope this helps Steve