It seems that there is a theme running through parshas Noach that involves opportunities granted after death to improve upon the mitzvos done during life. I am not an authority on such matters, and can only point out what I've seen and what I make of it.
1. Rav Chaim Falagi's peirush on Tehillim, in 33:14: ממכון שבתו השגיח אל כל ישבי הארץ. notes that the first letters of the first three words are משה, and the last three letters of those words are נוח, or, if you prefer, ונח. He says that Moshe was a gilgul of Noach's neshama. The Arizal says the same thing. They both note that Noach and Moshe were saved by being placed in a Teiva, which was floated upon the very medium that brought death to the others of their generation- Noach on the waters of the Mabul, which killed everyone of his generation, and Moshe on the waters of the Nile, into which the male children born at that time had been thrown to drown. Noach's neshama was given the opportunity to do its special mitzva a second time, and to do it properly this time Although Noach was a great Tzadik and beloved by Hashem, he was criticized for not doing enough to influence and save the people of his time. Moshe rectified this imperfection, because he, too, faced almost identical circumstances, but reacted very differently. When Klal Yisrael did the sin of the Eigel, Hashem told him that the people deserved destruction and that Moshe would be the only survivor who would begin a new race. Moshe did not accept this terrible gzeira. Moshe said that he cannot exist without the people he was responsible for. He said, Hashem, forgive the people, and if not, מחני נא, erase me from your book of life. The words מחני נא are an anagram for מנח אני. Hashem, this is my second chance. This time, I cannot live if my people die. If they die, I will die with them. (This idea is brought in many places: for example, it is in the Yalkut Reuveni in the beginning of Tetzaveh quoting the מגלה עמוקות, and in the Chasam Sofer's Drush for zayin Adar in 91)
I know less than nothing about gilgulim. What I see in this story is that שכר מצוה מצוה, and the reward of a mitzva, when it is done sincerely but imperfectly is the the opportunity to try to do it better. מצוה גוררת מצוה, and it can be gorer the ability to perfect it even after death.
2. Bava Kama 92b-
א"ל רבא לרבה בר מרי מנא הא מילתא דאמרי אינשי מטייל ואזיל דיקלא בישא גבי קינא דשרכי אמר ליה דבר זה כתוב בתורה שנוי בנביאים ומשולש בכתובים ותנן במתניתין ותנינא בברייתא כתוב בתורה דכתיב (בראשית כח) וילך עשו אל ישמעאל שנוי בנביאים דכתיב (שופטים יא) ויתלקטו אל יפתח אנשים רקים ויהיו עמו ומשולש בכתובים דכתיב [בן סירא יג] כל עוף למינו ישכון ובני אדם לדומה לו תנן במתני' כל המחובר לטמא טמא כל המחובר לטהור טהור ותנינא בברייתא רבי אליעזר אומר לא לחנם הלך זרזיר אצל עורב אלא מפני שהוא מינו
Rava said to Rabbah br'm, whence comes the expression "the inedible date goes strolling to settle in a copse of barren trees"? He said to him, this is stated in the Torah, the Neviim, the Kesuvim, the Mishna, and the Braisa.... Braisa - Reb Eliezer says "Not for nought does the Zarzir (starling) dwell with the raven. It is the same species (and equally impure/not kosher.)"
The Bechor Shor there in Bava Kamma, in the path of the Arizal, discusses the harmony of the relationship of the Dove/Yona with Noach, in contradistinction to his dissonant relationship with the Raven. He says that עופות טהורות, clean-species birds, are often to be found in the vicinity of Tzadikim. The reason is because they are souls that need a little elevation, and when the tzadik shechts them and does כיסוי הדם, and uses them to enable him to live and do mitzvos, this lifts up their souls. Noach, too, kept mitzvos of the Torah, and this is why the dove was closely associated with him.
נשמתן של רשעים מגולגלים בעופות טמאים, ויש נשמות צדיקים אשר צריכים איזה תיקון ומגולגלים בעופות טהורים, וע״י שנשחטה שחיטה כשירה ומכסים דמה בברכה זהו יקונה, ולכן נ״ל דדירתן עם הצדיקים, שבאותן עופות כון רק מתכוץ לשכון עם הצדיקים, ומתרץ ההוא משוס ובן אדס לדומה לו, פי׳ הבן אדם המגולגל באותו עוף הוא המתקרב לדומה לו
3. The first Rashi in the parsha, on 6:9:
אלה תולדות נח נח איש צדיק: הואיל והזכירו ספר בשבחו, שנאמר (משלי י ז) זכר צדיק לברכה. דבר אחר ללמדך, שעיקר תולדותיהם של צדיקים מעשים טובים: (This is from the Tanchuma here, Noach 2.)
These are the generations of Noah—Noah was a righteous man: Since Scripture mentions him, it tells his praise, as it is said (Prov. 10:7): “The mention of a righteous man is for a blessing.” - [Pesikta Rabbathi 12]. Another explanation [for why the names of the children are not mentioned immediately following “These are the generations of Noah”]: To teach you that the main generations [progeny] of the righteous are good deeds.
What does this mean, that the main progeny of Tzadikim is their good deeds? It certainly seems like a homiletic device that conveys the idea that children are the means by which we remain in the world even after we die, because we leave behind something important and lasting. For Tzadikim, their good deeds are so powerful that they change the world for the better, and so for them, their "progeny", the means by which they live after death because they continue to influence the world, is their good deeds.
But the Mahari Mintz, in his drashos, says that he once saw in the Zohar, based on the same theme as in this Rashi, that says that the widow of a tzadik that died childless really does not have the mitzva of Yibum. Yibum is only necessary for a person that died ובן אין לו, without child, but a tzadik has children - his good deeds are his children. His good deeds are more than children. The fact that in halacha such a woman does do yibum is only on behalf of some other lost soul of a person who was not a tzadik who died childless.
When I discussed this with my friends at my kiddush, I pointed out that while the story of Noach was the beginning of a story that culminated with Moshe Rabbeinu's saving the Jewish people, the story of Noach also echoes the experience of Adam in Gan Eden.
I am just pointing out parallels, not interpreting them.
1. When Noach came out of the Teivah, he was granted dominion over the animals, a dominion that expanded that which was given to Adam HaRishon.
2. Chazal see criticism in the words (9:20) ויחל נח איש האדמה ויטע כרם : Rashi- ויחל: עשה עצמו חולין, שהיה לו לעסוק תחלה בנטיעה אחרת: As a result of his chillul, וישת מן היין וישכר ויתגל בתוך אהלה , he drank and was exposed. I see here a connection, an echo, of the story of Adam HaRishon. Noach ate from an eitz, which happens to have been the grape (which the Zohar in Noach 307 associates with the Eitz HaDaas from Gan Eden,) and as a result, his nakedness was exposed. (The Malbim in 9:20-21 touches on this and distinguishes between Adam covering his nakedness and Noach's exposure.)
3. I speculated that while Adam and Chava were tantalized by the possibility of becoming greater through a more intimate access to knowledge, perhaps Noach sought a connection to ruchniyus through something beyond knowledge, the type of trance state that Neviim experienced. If so, both the chet of Adam HaRishon seeking knowledge, and the chet of Noach seeking something that required an abandonment of knowledge, were tainted by the immediate exposure of the animalistic component of the human state. (I gratefully acknowledge Rabbi Dr. Resnick's comments and observations.)
I repeat, this is not my area of expertise. I offer it only as something to think about.