Why does Rashi change Midrash Tanchuma?

A great post on DovBear, asking why Rashi changes the kiyor midrash.

That is, the pasuk and Rashi read like this (Shemot 38:8):

And he made the washstand of copper and its base of copper from the mirrors of the women who had set up the legions, who congregated at the entrance of the tent of meeting.		ח. וַיַּעַשׂ אֵת הַכִּיּוֹר נְחשֶׁת וְאֵת כַּנּוֹ נְחשֶׁת בְּמַרְאֹת הַצֹּבְאֹת אֲשֶׁר צָבְאוּ פֶּתַח אֹהֶל מוֹעֵד:
from the mirrors of the women who had set up the legions: Heb. בְּמַרְאֹתהַצֹבְאֹת Israelite women owned mirrors, which they would look into when they adorned themselves. Even these [mirrors] they did not hold back from bringing as a contribution toward the Mishkan, but Moses rejected them because they were made for temptation [i.e., to inspire lustful thoughts]. The Holy One, blessed is He, said to him, “Accept [them], for these are more precious to Me than anything because through them the women set up many legions [i.e., through the children they gave birth to] in Egypt.” When their husbands were weary from back-breaking labor, they [the women] would go and bring them food and drink and give them to eat. Then they [the women] would take the mirrors and each one would see herself with her husband in the mirror, and she would seduce him with words, saying, “I am more beautiful than you.” And in this way they aroused their husbands desire and would copulate with them, conceiving and giving birth there, as it is said: “Under the apple tree I aroused you” (Song 8:5). This is [the meaning of] what is בְּמַרְאֹתהַצֹבְאֹת [lit., the mirrors of those who set up legions]. From these [the mirrors], the washstand was made, because its purpose was to make peace between a man and his wife. [How so?] By giving a drink from the water that was in it [the washstand] to [a woman] whose husband had warned her [not to stay in private with a certain man] and she secluded herself [with him anyway. The water would test her and either destroy her or prove her innocence. See Num. 5:11-31]. You should know that they were actually mirrors, because it is said: “The copper of the waving was seventy talents… From that he made…” (Exod. 38:29, 30), but the washstand and its base were not mentioned there [among the things produced from the seventy talents. Thus,] you have learned that the copper of the washstand was not of the copper of the waving. So did Rabbi Tanchuma expound [on the matter] (Midrash Tanchuma, Pekudei 9; Num. Rabbah 9:14). And so did Onkelos render: בְּמֶחְזְיַתנְשַׁיָא [“the mirrors of the women”], which is the Aramaic translation of מַרְאוֹת, mirrors in French. So we find in Isaiah (3:23) וְהַגִּלְיֹנִים (sic), which we render: וּמַחְזְיָתָא, and the mirrors.		במראת הצובאת: בנות ישראל היו בידן מראות, שרואות בהן כשהן מתקשטות, ואף אותן לא עכבו מלהביא לנדבת המשכן, והיה מואס משה בהן, מפני שעשויים ליצר הרע, אמר לו הקב"ה קבל, כי אלו חביבין עלי מן הכל, שעל ידיהם העמידו הנשים צבאות רבות במצרים. כשהיו בעליהם יגעים בעבודת פרך, היו הולכות ומוליכות להם מאכל ומשתה ומאכילות אותם ונוטלות המראות, וכל אחת רואה עצמה עם בעלה במראה ומשדלתו בדברים, לומר אני נאה ממך, ומתוך כך מביאות לבעליהן לידי תאוה ונזקקות להם, ומתעברות ויולדות שם, שנאמר (שיר השירים ח ה) תחת התפוח עוררתיך, וזהו שנאמר במראות הצובאות. ונעשה הכיור מהם, שהוא לשום שלום בין איש לאשתו, להשקות ממים שבתוכו את שקנא לה בעלה ונסתרה, ותדע לך, שהן מראות ממש, שהרי נאמר (שמות לח כט ל), ונחשת התנופה שבעים ככר וגו', ויעש בה וגו', וכיור וכנו לא הוזכרו שם, למדת שלא היה נחשת של כיור מנחשת התנופה, כך דורש רבי תנחומא, וכן תרגם אונקלוס במחזית נשיא, והוא תרגום של מראות מירידויר"ש בלעז [מראות]. וכן מצינו בישעיה (ישעיה ג כג) והגליונים, מתרגמינן ומחזיתא:
who congregated: to bring their donation.		אשר צבאו: להביא נדבתן:

while the Midrash Tanchuma (Pekudei 9) reads like this:

אמרו הנשים: מה יש לנו ליתן בנדבת המשכן? 
עמדו והביאו את המראות והלכו להן אצל משה. 
כשראה משה אותן המראות, זעף בהן. אמר להם לישראל: טולו מקלות ושברו שוקיהן של אלו. 

המראות למה הן צריכין? 
אמר לו הקדוש ברוך הוא למשה: משה, על אלו אתה מבזה?! 
המראות האלו הן העמידו כל הצבאות הללו במצרים. טול מהן ועשה מהן כיור נחשת וכנו לכהנים, שממנו יהיו מתקדשין הכהנים, שנאמר: ויעש את הכיור נחשת ואת כנו נחשת במראות הצובאות אשר צבאו (שמ' לח ח), באותן המראות שהעמידו את כל הצבאות האלה. לפיכך כתיב: ונחשת התנופה שבעים ככר, נחשת הכלות. 
אמר הקדוש ברוך הוא: בעולם הזה נתנדבתם למשכן, שהוא מתכפר עליכם. 
ולעתיד לבא אני מכפר עליכם ואוהב אתכם נדבה, שנאמר: ארפא משובתם אוהבם נדבה (הושע יד ה). 
אמרו: אין לנו לא משכן לא מקדש, תהא לפניך תפלת פינו נדבת המשכן. 
אמר דוד: נדבות פי רצה נא ה' (תהלים קיט קח): 

Read carefully and see if you can spot the differences. DovBear spotted 3.

1. Tanchuma has Moshe say: break their legs, while Rashi omits
2. Rashi has Hashem say this is the best gift, while Tanchuma omits
3. Tanchuma has the kiyor for the purpose of sanctifying the kohanim, while Rashi has the kiyor for testing the Sotah.

Yet, Rashi credits Rabbi Tanchuma for this, saying כך דורש רבי תנחומא!

The way to resolve this is to look to the work Mekorei Rashi, from R' Yehuda Leib Krinsky (1840 - after 1915). Here is a picture of him:

He traces the sources (mekorei) of Rashi, and he is the first to turn to for questions like this.

He also credits Tanchuma 9, but in a slightly different manner:

Tanchuma ALEPH is different than our regular Tanchuma. It is the earliest Tanchuma, out of Tanchuma A, B, and C. Read up on it on Wikipedia:

Tanḥuma A is the collection published by S. Buber (Wilna, 1885), who gathered the material from several manuscripts. This collection, consisting of homilies on and aggadic interpretations of the weekly sections of the Pentateuch, is the oldest of the three, and Buber claimed that it was perhaps the oldest compilation of its kind arranged as a running commentary on the Pentateuch. It is even older than Bereshit Rabbah, which quotes several of its decisions. Buber postulated that this midrash (Tanḥuma) was edited in the 5th century, before the completion of the Babylonian Talmud, to which work it nowhere refers. Buber cites a passage in the Babylonian Talmud that seems to indicate that the redactor of that work had referred to the Midrash Tanḥuma. Other scholars disagree, however, and do not see the Buber recension of Tanchuma as being older than the other versions. Townsend cites a section from Buber's recension which appears to be a quote from Rav Sherira's Sheiltot (8th century). (ed. Townsend, Midrash Tanchuma, xii)

And this version, based on an Oxford manuscript, accords quite often with what Rashi says. Thus:

Tanhuma is one of the jewels of midrash literature. As one of the Yelammedenu midrashim, it is less diffuse than Genesis Rabbah, and its units are shorter than those of the Pesikta. It thus strikes a balance between the jumble of the one and the long sermons of the other. Just over a century ago, Solomon Buber published a new version of the Tanhuma based on an Oxford manuscript which is substantially different from the more common printed versions. It is this version or one very close to it which Rashi had before him and whose interpretations be often commends and recommends. Despite its importance and appeal, no version of Midrash Tanhuma has ever been translated into English. This volume is the first in a series which will bring the riches of the Buber edition to the English reader.

Alas, I cannot access this. Perhaps it is accessible on Bar Ilan, so that we can compare? If so, someone please post it in the comments.

I would guess that the resolution to many of these contradictions is in this, because (i) the bolded quote above, and because (ii) R' Yehuda Leib Krinsky explicitly pointed us to this version of the Tanchuma.