Might it be possible to think of this trial as being not narrowly an investigation of the effects of the actual prescription of puberty blockers, but, more broadly, the investigation of a treatment pathway that included such prescription as one of the theoretically possible outcomes?
In other words, the study is at least partly investigating whether the criteria for prescribing the meds would ever be met. Instead of viewing those criteria as the criteria for admission to the study, could we think of them as the criteria that must be met before studied children are prescribed puberty blocking meds?
In that case, the experiment is simply that of giving gender dysphoric children the adequate assessment, therapy, etc, that was lacking at Tavistock and seeing what the upshot of that would be. It would be a trial of puberty blockers only in the sense that they wouldn't be ruled out in advance, and would come into play if and only if it turned out that there ever were grounds for prescribing them.
If and only if there were ever grounds for prescribing them, the study would then have a second phase of long-term follow up of the effects of that decision.
That would make the study ethical, because it is essentially asking the question "What happens if you actually give these children the care that they need?"