Shalom!
Actually I have studied this a very long time ago. I don't' remember all what conclusions I came to except that when the ACCOUNT was written it was AFTER the L-RD established the months, the first being when they ( Israel) left Egypt which is called the first month, the month of Nissan. The month when Passover is (for those not familiar). So I don't think that there was any mix-up in months that was changed later.
Now the seventh month is the happiest month to me, for it starts with a warning ( Yom Teruah- Feast of trumpets) and then moves through the affliction of ones soul to 10 days later Yom Kippur - or the Day of Atonement. BUT when you come through this, out on the other side it is the Feast of Tabernacles! THE Holyday!!!!! and Rejoicing all week long!!! 
Now Tabernacles starts on the 15th of the month of Tishri, in 2 Chronicles it details how king Solomon brought up the ARK and placed it in the Temple and dedicated it during the Feast of Tabernacles. I can't find a specific day but maybe someone else here knows.
Another similarity can be drawn with the water libation ceremony and the prayers for rain during this time. For in Israel this is the beginning of the winter and rain is needed for the spring crops to come in. There was even a gate in the Temple that was named the Water gate and was used during this ceremony, the words of Isaiah were spoken "Therefore with joy you will draw water from the wells of salvation." Now the story of Noah is seen as one of salvation, saving out from water as is the story of Moses.
Now we can take this understanding from the calendar of Moses time or figure from other clues in the account in Genesis. We need to figure in all the time period to see what kind of calendar was used.
The account:
Genesis 7
1 And the LORD said unto Noah, Come thou and all thy house into the ark; for thee have I seen righteous before me in this generation.
2 Of every clean beast thou shalt take to thee by sevens, the male and his female: and of beasts that are not clean by two, the male and his female.
3 Of fowls also of the air by sevens, the male and the female; to keep seed alive upon the face of all the earth.
4 For yet
seven days, and I will cause it to rain upon the earth
forty days and forty nights; and every living substance that I have made will I destroy from off the face of the earth.
5 And Noah did according unto all that the LORD commanded him.
6 And Noah was
six hundred years old when the flood of waters was upon the earth.
7 And Noah went in, and his sons, and his wife, and his sons' wives with him, into the ark, because of the waters of the flood.
8 Of clean beasts, and of beasts that are not clean, and of fowls, and of every thing that creepeth upon the earth,
9 There went in two and two unto Noah into the ark, the male and the female, as God had commanded Noah.
10 And it came to pass
after seven days, that the waters of the flood were upon the earth.
11 In
the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.
12 And the rain was upon the earth
forty days and forty nights.
13 In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah's wife, and the three wives of his sons with them, into the ark;
14 They, and every beast after his kind, and all the cattle after their kind, and every creeping thing that creepeth upon the earth after his kind, and every fowl after his kind, every bird of every sort.
15 And they went in unto Noah into the ark, two and two of all flesh, wherein is the breath of life.
16 And they that went in, went in male and female of all flesh, as God had commanded him: and the LORD shut him in.
17 And the flood was forty days upon the earth; and the waters increased, and bare up the ark, and it was lift up above the earth.
18 And the waters prevailed, and were increased greatly upon the earth; and the ark went upon the face of the waters.
19 And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered.
20 Fifteen cubits upward did the waters prevail; and the mountains were covered.
21 And all flesh died that moved upon the earth, both of fowl, and of cattle, and of beast, and of every creeping thing that creepeth upon the earth, and every man:
22 All in whose nostrils was the breath of life, of all that was in the dry land, died.
23 And every living substance was destroyed which was upon the face of the ground, both man, and cattle, and the creeping things, and the fowl of the heaven; and they were destroyed from the earth: and Noah only remained alive, and they that were with him in the ark.
24 And the waters
prevailed upon the earth an hundred and fifty days.
Genesis 8
1 And God remembered Noah, and every living thing, and all the cattle that was with him in the ark: and God made a wind to pass over the earth, and the waters assuaged;
2 The fountains also of the deep and the windows of heaven were stopped, and the rain from heaven was restrained;
3 And the waters returned from off the earth continually: and
after the end of the hundred and fifty days the waters were abated.
4 And the
ark rested in the seventh month, on the seventeenth day of the month, upon the mountains of Ararat.
5 And the waters decreased continually until the tenth month: in
the tenth month, on the first day of the month, were the tops of the mountains seen.
6 And it came to pass at
the end of forty days, that Noah opened the window of the ark which he had made:
7 And he sent forth a raven, which went forth to and fro, until the waters were dried up from off the earth.
8 Also he sent forth a dove from him, to see if the waters were abated from off the face of the ground;
9 But the dove found no rest for the sole of her foot, and she returned unto him into the ark, for the waters were on the face of the whole earth: then he put forth his hand, and took her, and pulled her in unto him into the ark.
10 And he stayed yet
other seven days; and again he sent forth the dove out of the ark;
11 And the dove came in to him in the evening; and, lo, in her mouth was an
olive leaf pluckt off: so Noah knew that the waters were abated from off the earth.
12 And he stayed
yet other seven days; and sent forth the dove; which returned not again unto him any more.
13 And it came to pass in the
six hundredth and first year, in the first month, the first day of the month, the waters were dried up from off the earth: and Noah removed the covering of the ark, and looked, and, behold, the face of the ground was dry.
14 And in
the second month, on the seven and twentieth day of the month, was the earth dried.
Ok, new post to continue......................
