That's really interesting about delayed puberty being associated with ADHD. My family is kind of vying to be the poster child for genetic inheritance - multiple incidences of ADHD, ASD and bipolar going back lots of generations - and a very strong history of both delayed puberty and constitutional delay of growth. But we're all also ridiculously tall (the shortest man is 6ft 4"!) DD is an outlier even on the 85th.
It's very hard to sort chicken from egg as well. DD doesn't make endocrine IGF-1... the ignition switch for the body to use growth hormone. Not having IGF-1 seems to affect sleep and appetite - she didn't eat proper food till she was 3.5 years and has NEVER slept. Never napped as a baby, could go 48 hours without sleep, bedtime has been midnight since she was about 2 and I gave up the fight. However, no sleep and refusing to eat doesn't exactly do wonders for growth either! Spent years seeing the top experts in Europe and they never managed to find any answers - most kids with no IGF-1 have Laron Syndrome, which is a rare form of dwarfism. They'd only seen one other child like my DD who had no IGF-1 but didn't have Laron Syndrome.
Obviously the sleep issues were probably just as much down to the ADHD as the endocrine stuff.
So you just end up going round and round in circles!
I had no clue just how well DD would respond to methylphenidate either - having seen the results I feel so bad that we didn't start in primary as she'd probably be far more likely to hit her academic potential in terms of GCSE grades. Instead we're very much playing catch up (happily school are very much onside and supportive).
Plus on the social front, they do all seem to be very young for age - DD is so much more mature and rational on the meds than off! I am slightly envious that school get all that and I get the evening rebound and the unmedicated weekends... I feel your pain on that front!
Sorry not to have any solid answers - only thing I know for sure on growth stuff is that it take years and years of them just getting data and sometimes even after 10 years of appointments you still have no answers. Bone age x-rays were interesting though - we knew from those that she had plenty of catch-up as her bones were 4 years delayed from chronological age, which suggested she'd be at the taller end of their estimates.
It's not something that's easy to get doctors to do though as it's not always in best interests to irradiate children! Fascinating though it might be.
Wishing you lots of luck with it all - and the 11+ results!