How long did Moshe's mother carry him?

Not long ago, I ate with someone who mentioned Rashi on Exodus 2:3, which discusses the circumstances of Moshe's birth.

For those not in the know, here is the back story:

At around the time Moshe is conceived, Pharaoh decrees that all Israelite boy babies must be thrown into the river (1) Rather then risk losing a son, Moshe's parents initially separate, but reconsider and are reunited. (2) When Moshe is born, his mothers hides him for three months (3) after which, for some reason not supplied by the text, she is "no longer able to hide him" (4) Rashi suggests that Moshe was a seven-month baby (5) and because a seven-month baby can be born at six months and one day (6) gives the following gloss:

[When Moshe's mother] could no longer hide him: because the Egyptians counted her [pregnancy] from the day that [Amram] took her back. She bore him after [only] six months and one day  for a woman who gives birth to a seven-month child may give birth after incomplete [months]. And they searched after her at the end of nine [months].

The point being made here is that Moshe's mother was able to hide him for three months because he was born early. The Egyptians knew she was pregnant, and knew a baby would be arriving in, say, Adar; however because Moshe was born three months earlier in, say, Kislev,  his mother was able to hold on to him for three months.

The dinner table argument about this was ugly, and had to do with two simple facts:

• A child born at "six months and one day" doesn't survive without medical intervention, including drugs and oxygen. Though a rare 24-weeker can survive with medical assistance, they are very fragile, and almost never make it into adulthood without development difficulties. In antiquity, no 24-weeker could have survived.
• There's no such thing as a "seven-month" child. Human gestation is nine months, or forty weeks - no exceptions.

My dinner companion's response to all of this was the denial dance familiar to anyone who attempts to learn Torah with a fundamentalist. I was duly informed that Rashi knew everything, that he had something approaching the gift of prophecy, and that only a heretic would introduce medical evidence or personal experience against Rashi's word.

I countered in all the obvious ways, but it was to no avail. And here's the best part: On this verse Rashi is disagreeing with an aggadah as its recorded in the Talmud and its parallel in shmos raba:

She hid him three months. [She was able to do this] because the Egyptians only counted [the period of her pregnancy] from the time that she was restored [to her husband], but she was then already pregnant three months.

When I pointed this out to my friend, you could almost see his head explode. He attempted to reconcile Rashi with the aggadah in ways both humorous and sad, but ultimately left off insisting the Rashi had a better understanding of the midrash then we do. This is no doubt true; still seems clear that he went in another direction for reasons I hope to explain in the fullness of time.

NOTES

(1) Exodus 1:25 "And Pharaoh commanded all his people, saying, "Every son who is born you shall cast into the Nile, and every daughter you shall allow to live."
(2) The separation story is not in the text, but is a very old interpretation of various oddities in the verses.
(3) Exodus 2:2 "The woman conceived and bore a son, and [when] she saw him that he was good, she hid him for three months."
(4) Exodus 3:3 "And she could no longer hide him, so she took [for] him a reed basket, smeared it with clay and pitch, placed the child into it, and put [it] into the marsh at the Nile's edge"
(5) The idea, unsupported by medical evidence is that human beings have two types of pregnancy. Type 1 last nine months. Type 2 lasts seven months.
(6) Based not on medical evidence, but on an interpretation of I Sam. I, 20, Mar Zutra teaches on BT Niddah 38b that a nine-month baby can only be born after nine months, but a seven month baby can be born at anytime within the sixth month

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