I have no source for this answer, and I may very well be wrong, but here goes anyway:
Look at the expression Rashi brings: "ושרבב קומתו"
Now this word "ושרבב" rang a bell to me. Where is it used in other places?
1) Regarding the daughter of Pharoh who stretched out her hand - Rashi on Shemot 2:5
והם דרשו את אמתה את ידה, שנשתרבבה אמתה אמות הרבה:
They, however, interpreted אֶתאֲמָתָהּ to mean her hand, [that she
stretched out her hand,] and her arm grew many cubits (אַמוֹת) [so
that she could reach the basket].
2) Regarding the punishment of the 10 spies - Rashi on Bamidbar 14:37
באותה מיתה ההגונה להם מדה כנגד מדה. הם חטאו בלשון, ונשתרבב לשונם עד
Through that death which was fitting for them-measure for measure;
they had sinned with the tongue and now [in retribution] their tongues
extended to their navels.
So it seems to me that the word "שרבב" denotes growing/extending.
Furthermore, if we take the incident of the daughter of Pharoh:
We see that when someone has a good intention about something - even though it may be physically impossible - you should do your bit, and if Hashem Wills - He will cause you to succeed (via a miracle say)....
So too I could say about Yosef - Hashem make a miracle - and he grew tall to hide his mother from Eisav.
(again, no source, but I think it's a good pshat)