This is a great question, I found it almost exactly in Teshuvot Geone Batrae cited bellow. and I wrote a second answer based on this Shut. Here is my first draft.
1.Gemara Sanhedrin 57b fetus: "the man who is within the man" is a person:
בן נח נהרג ....
משום רבי ישמעאל אמרו: אף על העוברין .
On the authority of R`Ishmael it was said: [He (A Ben Noach) is executed] even for the murder of an embryo.
מאי טעמיה דרבי ישמעאל? דכתיב (בראשית ט') שפך דם האדם באדם דמו ישפך, איזהו אדם שהוא באדם - הוי אומר זה עובר שבמעי אמו.
What is R'Ishmael's reason? Because it is written, Whoso sheddeth the blood of man within [another] man, shall his blood be shed. What is a man within another man? - An embryo in his mother's womb.
2.Gemara Sanhedrin 72b, Mishna Ohalot 7, 6 Embryo life is less important than standard person live (the mother life and less important than the killer's life, if someone kills fetus, he is chayav mamon to the father and not exempt as he would be by kimleh bederaba mineh if fetus killing was chayav mita) .
אמר רב הונא קטן הרודף ניתן להצילו בנפשו קסבר רודף אינו צריך התראה לא שנא גדול ולא שנא קטן איתיביה רב חסדא לרב הונא יצא ראשו אין נוגעין בו לפי שאין דוחין נפש מפני נפש ואמאי רודף הוא שאני התם דמשמיא קא רדפי לה נימא מסייעא ליה רודף שהיה רודף אחר חבירו להורגו אומר לו ראה שישראל הוא ובן ברית הוא והתורה אמרה (בראשית ט) שופך דם שופך דם האדם באדם דמו ישפך, אמרה תורה: הצל דמו של זה בדמו של זה.
R'Huna said: A minor in pursuit may be slain to save the pursued. Thus he maintains that a pursuer, whether an adult or a minor, need not be formally warned. R'Hisda asked R'Huna: we learnt: Once his head has come forth, he may not be harmed, because one life may not be taken to save another. But why so?
Is he not a pursuer? - There it is different, for she is pursued by heaven. Shall we say that the following supports him? [Viz. ,] If a man was pursuing after his fellow to slay him, he (observer) says to him, 'See, he is an Israelite, and a son of the covenant, whilst the Torah hath said, Whosoever would shed the blood of a man, [to save] that man shall his own blood be shed, meaning, save the blood of the pursued by the blood of the pursuer'! - That is based on the ruling of R'Jose son of R'Judah.
3.We learnt a two Drashot from the words "Adam Baadam", Adam Baadam is an fetus. The din of chiuv mita for the murder of an embryo is only for Bene Noach, Gemara 57b told about Bene Noach, Rambam ruled it for Bene Noach excluding Jews (Shoftim, Melachim, 9, 4):
בֶּן נוֹחַ שֶׁהָרַג נֶפֶשׁ, אַפִלּוּ עֹבֶר בִּמְעֵי אִמּוֹ--נֶהְרָג עָלָיו. וְכֵן אִם הָרַג טְרֵפָה, אוֹ שֶׁכְּפָתוֹ וּנְתָנוֹ לִפְנֵי הָאֲרִי, אוֹ שֶׁהִנִּיחוֹ בְּרָעָב עַד שֶׁמֵּת--הוֹאִיל וְהֵמִית מִכָּל מָקוֹם, נֶהְרָג. וְכֵן אִם הָרַג רוֹדֵף שֶׁיָּכוֹל לְהַצִּילוֹ בְּאֶחָד מֵאֵבָרָיו--נֶהְרָג עָלָיו, מַה שְׁאֵין כֵּן בְּיִשְׂרָאֵל .
4.In Sanhedrin 72b Baadam is for the "by the man (the rodef would be killed by a man)".
5.the two drashot regard two different cases,
- The murder of an fetus.
the status of a fetus before it emerges [sic] is it a person?
- The fetus (not the the newborn) pursuing the mother.
6.The fetuse's life is sufficiently similar to life to punish Ben Noach who killed it, according to the Gemara 57b (from this verse Gemara learnt also general killing prohibition in bne Noach) .
7.The competition between the life of someone who already born and someone who has not yet been born is not an equal competition, two different kinds of life are compared. You asked in a comment
How does Shemot (Exodus) 21:22 fit with your answer "murder of an embryo"? (Shemot 21:22 says, "if men strive together, and hurt a woman with child, so that her fruit depart, and yet no [other] harm [to the woman] follow, he shall be surely fined," JPS.)
--> The answer is the same than with the Rodef, When the life of the murder is more valuable than the life of the dead (here the value of the life of the fetus is even less than a the life of a trefa man) there is no "nefashot case" not only because of edut sheyi ata yachol lehazima, but there is no chiuv mita. For a ben Noach there is a special stringency, for every sin he is chayav mita.
But I must admit that the SMA CM 425 and the Noda Bihuda CM tiniana 59, and the Teshuvot Geone Batrae agrees entirely with you.
If the childbirth migh kill the mother, the issue of Rodef begins.
if this fetus was only a piece of meat, there wouldn't be question of redifa, but the fetus has its own life, despite that he is not separated from mother body.
a fetus cannot be a rodef since it is part of the mother before it emerges
--> The Gemara in Sanhedrin 57b proofs that he is not really a piece of meat
The Gemara (according to Rashi's comment) said that as long as he is not born, despite that he is an other person, the lack of separated life eliminate the question of choice.
Sanhedrin 72B says a fetus becomes a person when its head emerges
--> That's not completely right.
8.The lack of what you called "free will" of the newborn is addressed by Gemara, his birth, his existence is not a free will and his life starting is the danger, Gemara called this situation (after the head exit but this is right even in the previous step) משמיא קא רדפי לה. Fetus (and new born) has no free will and they said Mishamaya Kararadfe lah. He is compelled to go out. Before head emergency, he has no independent life, this lack of separate life makes the superiority of the mother life beside fetus life, she has life and (mother life which is separated life is greater than non separated (from mother) life)
9.Parenthesis concerning "mishmaya karadfe lah" : For instance, idiocy is a lack of free will, which constitute a ptor in mitsvot for the idiot, but not for a rodef who is idiot, I wanted only to say that this "free will" is not fully contrary of mishmaya karadfey lah. A kind of will is referred by this expression, not "full will", but a multitude of possibilities. An idiot who pursues someone will be killed. But here the new born cannot, even randomly, make something else.
the status of a fetus before it emerges [sic] does it have free will?)
--> Not only he hasn't free will, but he also is not a Rodef he is just pushed. His redifa is not a real redifa after the maskana of the Gemara, because he also is pushed, "mishamaya Karadfe leih". But the Hava Amina of the Gemara was that there is no nuance between an idiot or a child who is pursuing someone with a gun. In maskana he is not a Rodef and there is no proof against Rav Huna. Despite the strange formulation of the Rambam, nezikin, rotseach 1, 9, who cited the word rodef for a fetus, Acharonim explained that this was not precisely his intent, see Teshuvot Geone Batrae 45 cited by the Leshed Hashemen in Rambam
Conclusion, Fetus has life, it is prohibited to kill it, Bene Noach are sentenced to death for this sin but not Jews. Concerning Rodef, the fetus-rodef's life is less valuable than the mother life which is already a separate life.