Re:
Not sure which Beinn has been outgrown but we have been looking at something similar. I guess the height is dependent on son / daughter given the age they grow. Our daughter is now several inches taller than the boys of her age she has grown up with.....
I've just built a Kona Hahanna 14" for the mrs as a single speed, so very small, more like 11" c-c. The Mrs is a tad under 5ft and my daughter who is also 12 is the same height. The Kona fits her well as well. I'm also building up a small Orange Prestige, which is more like 12" c-c which should be good for my daughter as she is long legged comparatively. It's just going to be another single speed as a second bike. 3 years ago she was still riding her Islabike Beinn 20 Large :shock: We spent ages looking at best next option. Beinn 24 was not going to last 5 minutes, the 26 seemed very expensive and second hand ones no better. In the end we went for a Frog 73. It's the only brand new bike she's had and will last a while. Actually the Frog 73 would make a great urban type bike on slicks for short adults. The Orange ss is more of a grab to go on short trips and not worry about leaving somewhere (locked of course but we do live in central london).
So in my mind find a very small frame and forks, fix other bits on, cranks need to be 170mm but 165 harder to find, and geared appropriately, single on the front and 7/8 on rear. Easy peasy, apart from finding frame of that size, expect to pay a premiun over one 2" larger !