According to the position in the gemara in Shabbos :צב that all of the leviim (includes cohanim) were 10 amos tall, how could Aaron or Moshe fit in the Ohel Moed (10 Amos tall as well, see parshas Teruma) standing straight and wearing tefillin and the mitznefes above their heads? Magnifying the question, Tosfos (and seemingly all of the rishonim other than the Rashbam in Bava Basra) holds that ten amos is just until his neck (and with his head he was 10 1/2 amos tall), and this was his height before having the shemen hamishcha, which according to many, we see from Dovid hamelech made people grow taller?
The Aron did not take up any room as it says Yoma 21a and Megila 10b.
Likewise we find in Avos 5,5 עומדים צפופים ומשתחוים רווחים they stood in the Bais Hamikdash squashed and bowed down with space.
So too with Aharon and Moshe - who were 10 Amos tall not including the Mitznefes, which made them taller - didn't suddenly bang their heads because their presence took up less space relative to the Mishkan which made space when it was needed. The Alshich in Eicha (Lamentations) 4,12 explains (see hebrew books) that there are no boundaries of space in the Sanctuary because it is an area in this world that is shared with the upper Realms Where Hashem Dwells which is Ruchni (Metaphysical) and do not have space constraints. Hashem is infinite and still encapsulates within the Mishkan/Beis Hamikdash.
An alternative answer is The Malbim commentary on Maseches Shabbos 92a which says that Moshe and the cohanim/levied who carried the mizbeach were able to miraculously change height according to the task at hand but their height was that of a regular person. So Moshe for example was only 10 Amos high to set up the planks which were ten Amos but once he went into the mishkan to serve he was back to a regular height.
Aharon and Moshe were not giants. These are metaphors and stories that have been taken literally. Many Rishonim have spoken about what a shame it is that people take aggadot literally when they are usually either speculation or meant to convey sodot. Very rarely are they literally true. In this case Aaron is obviously not 10 amot tall. Og's bed was 9 amot by the Torah's words, implying that was his height, now how did Moshe, who is taller than him, jump and only reach his ankle?
The blessed Rambam's thoughts on the matter:
The first class is, as far as I have seen, the largest in point of their numbers and of the numbers of their compositions; and it is of them that I have heard most. The members of this class adopt the words of the Sages literally, and give no kind of interpretation whatsoever. With them all impossibilities are necessary occurrences. This is owing to their being ignorant of science and far away from knowledge. They do not possess that perfection which would spur them on of their own accord, neither have they found any means for rousing their attention. They think that in all their emphatic and precise remarks the Sages only wished to convey the ideas which they themselves comprehend, and that they intended them to be taken in their literalness. And this, in spite of the fact that in their literal significance some of the words of the Sages would savour of absurdity. And so much so that were they manifested to the ordinary folk (leave alone the educated) in their literalness, they would reflect upon them with amazement and would exclaim: “How can there exist any one who would seriously think in this way and regard such statements as the correct view of things, much less approve of them.” This class of men are poor, and their folly deserves our pity. For in their own opinions they are honouring the Sages, whereas in reality they are all the time degrading them to the lowest depths—and this all unconsciously. As God lives, it is this class of thinkers that robs our religion of its beauties, darkens its brilliance, and makes the Law of God convey meanings quite contrary to those it was intended to convey...
-Rambam, Introduction to Mishnah Tractate Sanhedrin, chapter 10 (Perek Helek)
This is asked by Moshav Zekeinim (Shemos 26:1), brought by Tosafos HaShalem (Shemos 26:16 § 7), and by the Shita Mekubetzes HaShalem on Bechoros 44a s.v. משה רבינו. They don't really answer it.
Rav Chaim Kanivesky in his Ta'amah D'Krah brings an answer that they would deepen the ground under the Mishkan. He likes this answer.
Practically speaking, they simply could have crouched or slouched a little bit.
(Note that if the entire Limmud is from the fact that Moshe was able to cover the top of the Mishkan, and that therefore he must have been as tall as it, there is no way that we can change the measurements, as some others have attempted to do.)
There is a source that states that Aharon was only 3 amos tall. This is based on the fact that he needed steps to light the Menorah, which was just over 18 tefachim high (not including the neros).
Of course, Moshe and Aharon weighing the same (מלמד ששקולים היו), this implies that Aharon was very wide at the girth.
Source: Sefer Beis Asher (al HaTorah), Parshas Pikudei, quoting a conversation between the Bnei Yisoschor and R' Hersh of Ziditchov, cited by Minhag Yisrael Torah. The vort is on the verse ויפרש את האוהל על המשכן, "and [Moshe] spread the Ohel [cover layer] on the Mishkan."
(Yes, this vort about Moshe's height and Aharon's girth is metaphorical - "רזין דאורייתא", to quote R' Hersh about the above mentioned conversation - and the Beis Asher explains it בדרך רמז, by way of allusion.)
Units of measure can have different values in different settings (eg a dozen is 13 in a bakery and a Troy ounce is not the same as an ounce). So too, there is a long cubit and a short cubit.
I recall that the units of the mishkan were ,10 percent larger than regular units so Aaron could be 10 ammot and the mishkan could be 11.
Apparently, in Egypt they had a royal cubit, 1/6 larger.