I have found a beautiful commentary concerning this amongst the writings of the Arizal. We must understand why Moses bothered to set aside these three cities, seeing they could not perform their function until the other three cities of refuge on the West Bank of the Jordan had been set aside also (Numbers 35,13; compare Makkot 9). When we understand the Arizal's commentary on the problem of the cities of refuge, we will also understand why the Torah interrupted the report about the gift of the Torah to the Jewish people by mentioning already at this point that Moses set aside the three cities of refuge which were to be on the East Bank of the Jordan. The Ari zal sees in Moses' action an attempt at rehabilitation for when he had committed manslaughter and had taken it upon himself to slay the Egyptian who had tortured a Jew (Exodus 2,12). He had considered this killing in the category of a murder inadvertently committed because he had felt at the time that he was performing a מצוה by doing so. The first letters of the words הירדן מזרחה שמה, which describe what Moses did, form the acronym משה. The following words, אשר ירצח את רעהו are also an allusion to Moses. We have already described that Moses was the re-incarnation of Abel. The Torah here alludes to the first murder i.e. fratricide, when Cain slew his brother Abel. This is also alluded to in Exodus 2,11, when the Torah describes Moses as observing an Egyptian man: מכה איש עברי מאחיו, "torturing a Jewish man, one of his brothers." The Torah hints that the Egyptian was a former brother of Moses, i.e. a re-incarnation of Cain. In this instance the evil which had been part of Cain's character had re-surfaced in the character of this Egyptian. We have explained on another occasion that the נפש of Cain, i.e. his lowest spiritual part, was re-incarnated in the body of this Egyptian, whereas Cain's רוח, the superior part of his soul, was re-incarnated in the body of Yitro. The highest part of Cain's soul, i.e. the נשמה, was re-incarnated in the body of Korach. Korach made the mistake of quarrelling with Moses; this resulted in his גלגול failing to achieve its ultimate purpose. Yitro was of mixed feelings. When he became aware that he was wrong, had sinned, he converted to Judaism. At the end of the paragraph dealing with the cities of refuge the Torah writes: וזאת התורה אשר שם משה. This means that Moses determined the need to set aside these three cities of refuge at this time for his own sake.
It was among the possessions of these two and a half tribes also that Moses shortly before his death founded the cities of refuge. Moses in this instance illustrates the proverb, "Whosoever loves pious deeds, never has enough of them." Although God had told Moses that he would never cross to the other side of the Jordan, he still insisted upon at least determining the site for the asylum in the region of the East Jordan. God gave Moses the law concerning the cities of refuge in accordance with Israel's wish. For the people said to God: "Lord of the world! Thou didst promise us a long course of life as a reward for fulfilling the commandments, but supposing now that a man hath slain another unintentionally, and the avenger of the blood slays him, he will die before his time." God then said to Moses: "As truly as thou livest, they speak wisely. Appoint therefore several cities for cities of refuge, 'that the manslayer might flee thither, which slayeth his neighbor unawares.'" Moses rejoiced greatly at this statute, and instantly set about its execution, for "he that hath tasted of a food knoweth its flavor," and Moses who had erstwhile been obliged to flee on account of having slain an Egyptian, knew the feelings of the man who is pursued on account of a manslaughter that he had committed unawares.
וְהִקְרִיתֶם לָכֶם עָרִים (במדבר לה, יא), זֶה שֶׁאָמַר הַכָּתוּב (תהלים כה, ח): טוֹב וְיָשָׁר ה' עַל כֵּן יוֹרֶה חַטָּאִים בַּדָּרֶךְ. (תהלים כה, ו): זְכֹר רַחֲמֶיךָ ה' וַחֲסָדֶיךָ, אָמַר דָּוִד רִבּוֹנוֹ שֶׁל עוֹלָם אִלּוּלֵי חֲסָדֶיךָ שֶׁקָּדְמוּ לְאָדָם הָרִאשׁוֹן לֹא הָיָה לוֹ עֲמִידָה, שֶׁנֶּאֱמַר (בראשית ב, יז): כִּי בְּיוֹם אֲכָלְךָ מִמֶּנּוּ מוֹת תָּמוּת. וְלֹא עָשִׂיתָ לוֹ כֵן אֶלָּא הוֹצֵאתָ אוֹתוֹ מִגַּן עֵדֶן וְחָיָה תְּשַׁע מֵאוֹת וּשְׁלשִׁים שָׁנָה, וְאַחַר כָּךְ מֵת. מֶה עָשִׂיתָ לוֹ, גֵּרַשְׁתָּ אוֹתוֹ מִגַּן עֵדֶן, שֶׁנֶּאֱמַר (בראשית ג, כד): וַיְגָרֶשׁ אֶת הָאָדָם. וְלָמָּה נִתְגָּרֵשׁ עַל שֶׁהֵבִיא מִיתָה עַל הַדּוֹרוֹת וְהָיָה חַיָּב לָמוּת מִיָּד, אֶלָּא שֶׁרִחַמְתָּ עָלָיו וְגֵרַשְׁתּוֹ, כְּדֶרֶךְ הָרוֹצֵחַ בִּשְׁגָגָה שֶׁגּוֹלֶה מִמְּקוֹמוֹ לְעָרֵי מִקְלָט, לְכָךְ נֶאֱמַר: זְכֹר רַחֲמֶיךָ ה' וַחֲסָדֶיךָ וגו', כֵּיוָן שֶׁעָמַד משֶׁה וְאָמַר לוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא וְהִקְרִיתֶם לָכֶם עָרִים, אָמַר משֶׁה רִבּוֹנוֹ שֶׁל עוֹלָם, זֶה שֶׁהָרַג נֶפֶשׁ בִּשְׁגָגָה בַּצָּפוֹן אוֹ בַּדָּרוֹם, מִנַּיִן יוֹדֵעַ הֵיכָן עָרֵי מִקְלָט שֶׁיְהֵא בּוֹרֵחַ לְשָׁם, אָמַר לוֹ (דברים יט, ג): תָּכִין לְךָ הַדֶּרֶךְ, תְּכַוֵּן לְךָ הַדֶּרֶךְ שֶׁלֹא יִהְיוּ טוֹעִים וְיִמְצָא אוֹתוֹ גּוֹאֵל הַדָּם וְיַהַרְגֵּהוּ (דברים יט, ו): וְלוֹ אֵין מִשְׁפַּט מָוֶת. עוֹד אָמַר לוֹ, הֵיאַךְ, אָמַר לוֹ הַעֲמֵד לָהֶם אִיסְטְלָיוֹת מְכֻוָּנוֹת לְעָרֵי מִקְלָט, שֶׁיְהֵא יוֹדֵעַ לֵילֵךְ שָׁם, וּבְכָל אִיסְטְלָיוֹת רְשֹׁם עָלֶיהָ רוֹצֵחַ לְעָרֵי מִקְלָט, שֶׁנֶּאֱמַר תָּכִין לְךָ הַדֶּרֶךְ. לְכָךְ אָמַר דָּוִד: טוֹב וְיָשָׁר ה' עַל כֵּן יוֹרֶה חַטָּאִים בַּדָּרֶךְ. אִם לְרוֹצְחָנִין עֲשֵׂה שְׁבִיל וְדֶרֶךְ שֶׁיִּבְרְחוּ וְיִנָּצְלוּ, לַצַּדִּיקִים עַל אַחַת כַּמָּה וְכַמָּה, (תהלים כה, ט): יַדְרֵךְ עֲנָוִים בַּמִּשְׁפָּט וִילַמֵּד עֲנָוִים דַּרְכּוֹ. (במדבר לה, יא): וְנָס שָׁמָּה רֹצֵחַ מַכֵּה נֶפֶשׁ בִּשְׁגָגָה, וְלֹא בְזָדוֹן, וְאִם יַהֲרֹג בְּזָדוֹן וְיֹאמַר בִּשְׁגָגָה הָרַגְתִּי וִיהֵא בּוֹרֵחַ לְעָרֵי מִקְלָט, אָמַר הַקָּדוֹשׁ בָּרוּךְ הוּא אֲפִלּוּ בּוֹרֵחַ וְנִכְנַס בַּמִּזְבֵּחַ שֶׁלִּי הִרְגּוּ אוֹתוֹ, שֶׁנֶּאֱמַר (שמות כא, יד): וְכִי יָזִד אִישׁ עַל רֵעֵהוּ וגו' ...
"And you shall provide yourselves with cities" (Numbers 35:11), this is what the verse says, "Good and upright is the Lord, therefore He shows sinners the way." (Psalms 25:8) "Remember Your mercy, O God, and your lovingkindness." (Psalms 25:6). David said, Master of the Universe, were it not for the fact that Your lovingkindness preceded the First Man, he would not have been able to stand, as it says "For the day you eat of it [the tree of knowledge of good and evil] you will surely die" (Genesis 2:17). And You did not do this; rather, You brought him out from the Garden of Eden and he lived for 930 years(!) and only after that did he die. Why did you do that to him, to drive him out from the Garden of Eden, as it says (Genesis 3:24) "and He drove out the man"? Why was he driven out, since he brought death upon the generations, and he was sentenced to immediate death? Rather, You had mercy upon him and drove him off, just as the accidental killer is exiled to a city of refuge. Thus it says, "Remember Your mercy, O God, and Your lovingkindness, etc." Once Moshe stood and the Holy Blessed One told him, "Provide yourselves with cities...", Moshe said "Master of the Universe, this one killed by accident in the south or the north; how will he know where the city of refuge is, that he may flee to it?" God replied, "'Set for yourselves the path... [i.e. to the cities of refuge]' (Deuteronomy 19:3), orient for yourselves the path so that you will not be mistaken and find the blood avenger and he will kill you "and there will be for him no death penalty" (Deuteronomy 19:6)." He [Moshe] said again, "How?" He [God] said to him, set up for yourselves signs [istlayot] pointing to the cities of refuge, that they will know where to travel. And on every sign write "Killer to the city of refuge", as it says "prepare for yourselves the way". Thus said David, "Good and upright is the Lord, therefore He shows sinners the way." If for killers He makes a path and a road for them to flee by and be saved, all the more so for righteous! "He guides the humble in justice, and teaches the humble His way" (Psalms 25:9). "And the killer shall flee there who has killed a soul by accident" -- but not on purpose. If he kills on purpose and he says "I accidentally killed" and flees to the cities of refuge, the Holy Blessed One says, even if he flees and enters to My altar, you shall kill him, as it says (Exodus 21:14) "And if a person schemes, etc [against another, and kills him treacherously, you shall take him from My very altar to be put to death]". ...
…דבר אחר: "אז יבדיל משה" – מהו 'אז'? זה שירה, שנאמר (שמות טו): "אז ישיר משה". מי אמר שירה? משה אמר שירה. למה? שהוא הרג את הנפש. "ויך את המצרי". וכיון שהרגו ברח לעיר מקלט, שנאמר: "ויברח משה מפני פרעה וישב על הבאר… ולמה אמר שירה? שהוא היה יודע צערו של רוצח… וכיון שאמר ליה הקב"ה רפואתו, התחיל משה אומר שירה , שנאמר: "אז ישיר משה" -- דברים רבה (ליברמן), ואתחנן.
When the verse says “Then Moses set apart,” what is meant by “then?” It is a song, as we saw “and then sang Moshe” (Shemot 15:1). And who sang? Moshe sang. Why? Because he had killed a person.
[fill this in]
And why did he sing? For he knew the pain of the killer... and when God said to him "you are healed" Moshe began to sing, as it says "Then Moshe sang"
-- Deuteronomy Rabbah, Parshat Va'etchanan, Lieberman edition