Why did Moshe translate the Torah into 70 languages?

In parashat Devarim, the following pasuk and Rashi:

On that side of the Jordan, in the land of Moab, Moses commenced [and] explained this Law, saying,

ה. בְּעֵבֶר הַיַּרְדֵּן בְּאֶרֶץ מוֹאָב הוֹאִיל משֶׁה בֵּאֵר אֶת הַתּוֹרָה הַזֹּאת לֵאמֹר:

explained this Law: He explained it to them in seventy languages. [from Midrash Tanchuma 2; Gen. Rabbah 49; see Sotah 32a). Hakethav Vehakabbalah explains this to mean that Moses gave them seventy interpretations to every passage.

באר את התורה: בשבעים לשון פירשה להם:

It is not only Chabad's translation that refers us to HaKsav veHakabbalah. See also Ateres HaMikra:

Q: Didn't the Israelites only understand Hebrew, and perhaps some of them also Egyptian? If so, why explain the Torah in 70 languages? 

A: (HaKsav veHakkabalah) The 70 languages are '70 intentions', as Chazal say, there are 70 facets to the Torah. (Midrash Rabbah, Bemidbar 13:15) 

A: (Ateres) Perhaps we can explain that Moshe transmitted to them secrets of the Torah as is brought (Aggadas Bereishis 15:1) 'Sod Hashem Liyrei'av', סו"ד is the gematria of 70.

haKsav vehaKabbalah

You can read HaKsav veHakkabalah inside here. It is interesting that he assumes that the Israelites are the only possible targets, rather than the other nations of the world. And then, based on lack of any simple explanation of this midrash, this passage becomes cryptic, and becomes either metaphorical or mystical. Seventy can refer to 70 facets, even though elsewhere there is a tradition of 70 nations and 70 languages. (Haksav veHakkabalah connects the two, citing a Raya Mehemna that the Sanhedrin knowing 70 languages as the 70 facets of Torah.)

While this is plausible, and works well with the word באר, a good alternative approach is to scour Chazal to see whether they themselves give an explanation. And they do. In the Yerushalmi to the aforementioned Mishna in Sotah, we read:

דף לב, א פרק ז הלכה ה משנה  ואח"כ הביאו את האבני' ובנו את המזבח וסדום בסיד וכתבו עליהם את כל דברי התורה הזאת בשבעים לשון שנאמר (דברים כו) באר היטב ונטלו את האבנים ובאו ולנו במקומן: 

דף לב, א פרק ז הלכה ה גמרא  תני על אבני המלון נכתבו דברי רבי יודה.  רבי יוסי אומר על אבני המזבח נכתבו.  מאן דמר על אבני המלון נכתבו בכל יום ויום אומות העולם משלחין נוטריהון ומשיאין את התורה שהיתה כתובה בשבעים לשון.  מאן דמר על אבני המזבח נכתבו לא לשעה היו ונגנזו.  עוד הוא מעשה נסים.  נתן הקב"ה בינה בלב כל אומה ואומה והשיאו את התורה שהיתה כתובה בשבעים לשון.

Or, in the Tosefta, also on Sotah:

ח,ה  ר' יהודה אומר על אבני [המזבח כתבום אמרו לו] האיך למדו [אותם] עובדי כוכבים את התורה אמר [להם] מלמד שנתן [המקום] בלב כל אומה ומלכות והשיאו את הכתב מגבי האבנים בשבעים לשון באותה שעה נתחתם גזר דינן של עובדי כוכבים לבאר שחת ר"ש אומר על הסיד כתבו כיצד כידוהו וסידוהו בסיד וכתבו עליו את כל דברי התורה בע' לשון וכתבו [מלמטה] (דברים כ) למען אשר לא ילמדו אתכם וגו' אם אתם חוזרין בכם אנו מקבלין אתכם.

In both cases, we see that the gentiles, the umos ha'olam could be recipients of the Torah.

We have a much easier time nowadays finding these obscure sources. It is a simple Snunit search, or following a reference to the Mishna in Sotah and deciding to check out what the Bavli, Yerushalmi and Tosefta have to say about it.

I wonder also if there is a mental block in place, in which the assumption would be that any translation would be directed inward, towards the Jews, rather than outward, as a light unto the nations.

Perhaps see Rabbi Jonathan Sacks recent essay, A Judaism Engaged With The World.

Certainly see also the Tanchuma, which reads a different interpretation into this feat of Moshe, as showing a transition from Moshe as not an ish devarim.

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Here is another idea. It might not match the intent of the author of the midrash, but it sort of bridges these two explanations. Translation is interpretation. Here is a recent interview with Robert Alter that makes that point:

Every great work of literature – and there’s much great writing in the biblical Hebrew – has a mastery of means in its own language. It’s not only the kind of perfect word choice and subtle shifts from one level of the language to another, but also the rhythms, the lengths of words, etc. When you’re translating, you can’t possibly get all of those, while all the different features come together in perfect harmony in the original language. In most cases, you decide what’s less important and you sacrifice something: maybe you don’t focus on the order of the words in order to achieve some other effect of the original that’s important; maybe I can get the rhythm of the language but not quite the English equivalents that have the exact same resonance as the original.

Multiple translations might do a better job at capturing the nuance.