Hi LittleWhiteMan, I'm one of those 'lucky guys' at 5'7"(actually more 5'6.5"). However, that's where my 'luck' ends ;-) I may have 5.5" (14 cm) more bodyheight, but have only 7 cm more sitting height. So my leg length (floor inseam) is about 33" (84 cm), wich is just under 50%. I too have the torso of a 12 - 13 year old child with narrow shoulders and I'm skinny/lanky built. At your age (16) I was about your height (don't know exactly anymore) but I do know, I grew until my early twenties, gaining leg length only. Buying clothes today always ends in the junior department, including the preprogrammed disappointment of short arms and not to speak far too short legs ;-( Ok, at least the T-shirts fits ;-)
Living in 'tall country' the Netherlands, my dream height is still around 6' or 6'1". This even after reading in recent official statistics that the height increase of the past decade has ended and the youngest generation is even decreasing a little in average bodyheight - yes, ethnic corrected!
Will LL to do for me? Many aspects to consider! Desired body height is simple. 6' may be 6'1". Would require 5" to 6" height increase. An amount of LL that make sense to me. Wich would bring me however to a floor inseam of 38"or even 39". Such leg lenghts are not only disproportional at 6'/6'1" (53%) but where to buy any trousers in that inseam at a waist of 26? (Yeah, I wouldn't mind becoming average at 6'2" or 6'3" but would make me a total freak.)
So, doing less LL? Going from 5'6.5" to let's say 5'9" or 5'10" (below Dutch average, but both nice heights) means doing 2.5" or 3.5". LL of 3.5" in one segment could however japardize my femur-tibia ratio. Doing 3.5" in two segments is, from a view point of costs and efforts, out of the question. Doing only 2.5" in one segment, would bring me at 5'9".
Arm lenght is another story. I don't see it as a problem that my arms stay relatively short (compared to body height) after LL (even doing 3.5"). In my view it's more important to have an arm length that fits with my torso than with my body height. Some (professionally Photoshoppped) mock ups of guys with long legs, but arms in harmony with their torsos, underlined my view. But feel free to disagree!
So - that's where we share the same f**kted body proportions.