This is MMM's answer. He has already uploaded the patched tikzscale package to ctan. I will open a bounty later, in his answer that led to this package, to express my appreciation to MMM's work on this package and his speedy reply. It was a little late in posting this but I hope that you can still benefit from the information here.
MMM's answer
Don't you get the correct tree as output at all? When using a slightly
adapted size (otherwise the height of the tree is too large to fit on a
page) like in
\includegraphics[width=0.9\linewidth]{mytree.tikz}
I get the attached output file, which is the correct tree, I think. If you
do not get this output, please use the attached sty-file* and a recent
development variant of TikZ/PGF.
* Download the patched package in ctan instead
Although the tree is correct, the size of the nodes (with the meaning of
edges and nodes, i.e. graph speech) is very large, which is, what tikzscale
wants to avoid normally. tikzscale normally uses the tikzpicture's scale
option to iteratively converge to the correct size as in \begin{tikzpicture}[scale=4].
This works, as TikZ/PGF defines, that scaling does not scale nodes (with the
meaning of coordinates and nodes, i.e. TikZ speech). Unfortunately, the
tikz-qtree package seems to ignore that definition. I am not sure, if that
was done on purpose (I've CC'ed its author), but I do not think that
tikzscale can do much as long as tikz-qtree does this scaling.
Did you have a look at the graph chapter in a recent development version of
TikZ/PGF? I think these graphs behave correctly regarding scaling, which
basically means, that they are unscalable at the moment.
You can try using code like the following
\makeatletter
\ifdef{\tikzscale@scale}{%
% This is not commutative, as there is an error on commutation!
\pgfmathsetlength{\parts}{\textwidth * \tikzscale@scale}%
}{}%
\makeatother
to get a dynamically sized variable \parts, which can be used to set the
node distance or something like that, to get a graphic which is scalable
with tikzscale, but this is all not officially supported, yet. Nevertheless,
I would be interested to hear about use cases.
About the tikz-qtree
The author has expressed interest in fixing the scale implementation as suggested by MMM.