A resolution for Rashi's awkward על ידי שבשביל ש?

Summary: I would say not. While slightly awkward, the sentence parses as it stands, and makes perfect sense. Yosef Daas suggests a radical reinterpretation based on manuscript evidence, that על יד means immediately, and Rashi is making two separate points, but I don't find this suggestion compelling.

Post: The law of the hammer is popularly phrased as ""if all you have is a hammer, everything looks like a nail." Even when other approaches may be more effective, one is tempted to use that hammer.

The first Rashi on Vayeitzei reads:

10. And Jacob left Beer sheba, and he went to Haran.		י. וַיֵּצֵא יַעֲקֹב מִבְּאֵר שָׁבַע וַיֵּלֶךְ חָרָנָה:
And Jacob left: Because, it was due to the fact that the daughters of Canaan were displeasing in the eyes of his father Isaac, that Esau went to Ishmael, Scripture interrupted the account dealing with Jacob and it is written (above verse 6): “When Esau saw that Isaac had blessed [Jacob], etc.” And as soon as Scripture finished [the account of Esau’s marriage], it returned to the previous topic.		ויצא יעקב: על ידי שבשביל שרעות בנות כנען בעיני יצחק אביו הלך עשו אל ישמעאל, הפסיק הענין בפרשתו של יעקב וכתיב (לעיל כח ו) וירא עשו כי ברך וגו', ומשגמר חזר לענין הראשון:

The phrasing of על ידי שבשביל ש seems duplicate and awkward, and this prompts many meforshei Rashi to analyze what Rashi is doing. In fact, it is not duplicate and only slightly awkward. The בשביל ש introduces the causal statement of: because the daughters of Canaan were displeasing in Yitzchak's eyes, Esav went to Yishmael. And the על ידי ש introduces the causal statement of: because of Esav's action, Scripture interrupted the account dealing with Yaakov. Thus, this ויצא יעקב is a return to the previous topic. This straightforward reading of Rashi is also more or less what Gur Aryeh says. This Rashi does not cry out "darshen me". See what other meforshei Rashi say. (I haven't yet, but it seems to be a topic of conversation.)

Yosef Daas, by R' Yosef ben Yissachar Miklish of Prague, a dayan of the Beit Din of Prague, 1580-1654), printed in Prague in 1609, is a wonderful supercommentary on Rashi that considers manuscript evidence. Here, he writes:

"I found a correction in Rashi, that the yud is erased from the word ידי, and one must then say על יד. And its meaning is this: That it is difficult to Rashi za'l why he [Yaakov] did not go immediately [מיד] after Rivka's command. And upon this Rashi explains that the meaning of the word ויצא is על יד. That is to say, immediately [מיד] after the command. And if so, why does it interrupt with וירא עשו, etc.? Upon this he explains "שבשביל".

I have found this. And one who wishes to lose the find, he has permission to do so, and no one will either prevent or compel him."

My preference would be to lose this metziah. Even if the word ידי is missing the final yud, על יד would still mean 'because', rather than immediately. We should not take Rashi away from his plain meaning, which makes perfect sense as it stands.