Known to your tribes -- against the trup?

In the beginning of Devarim, we have:

יג הָבוּ לָכֶם אֲנָשִׁים חֲכָמִים וּנְבֹנִים, וִידֻעִים--לְשִׁבְטֵיכֶם; וַאֲשִׂימֵם, בְּרָאשֵׁיכֶם.

13 Get you, from each one of your tribes, wise men, and understanding, and full of knowledge, and I will make them heads over you.'

Rashi is repeatedly channelling Sifrei here, and so he cites what is obviously a midrash as his perush. The interesting thing is that this midrash would seem to be against the trup. Thus, Rashi writes:

well-known among your tribes: Men whom you recognize, for if one were to come before me wrapped in his tallith, I would not know who he is and of what tribe he is, and whether he is suitable. But you know him, for you have raised him. Therefore, it says,“well-known among your tribes.” (Sifrei)

וידועים לשבטיכם: שהם ניכרים לכם, שאם בא לפני מעוטף בטליתו איני יודע מי הוא ומאיזה שבט הוא ואם הגון הוא, אבל אתם מכירין בו, שאתם גידלתם אותו, לכך נאמר וידועים לשבטיכם:

Thus, viyduim connects with leshivteichem.

In contrast, Ramban presents an explanation more in line with the peshat. He writes:

יג): וידעים לשבטיכם -

שהיו ניכרים לכם, שאם בא לפני מעוטף בטליתו איני יודע מי הוא ומאי זה שבט הוא, אבל אתם מכירים אותו שגדלתם אותו, לשון רש"י מספרי (דברים יג).

ואם כן, יהיה "לשבטיכם" קשור עם "וידועים".

אבל על דרך הפשט טעמו, הבו לכם לשבטיכם אנשים חכמים.

ועל דעתי, טעם "וידועים" שהם ידועים לשופטים, כלומר שמעלתם ידועה ונכרת למנותם בה שופטים. וכלל מעלות השופטים במלת "וידועים", כי השופטים צריכין להיות אנשי חיל יראי אלוהים אנשי אמת שונאי בצע כאשר אמר יתרו, ואלה היו ידועים לשופטים מתחלה כי היו הכל אומרים ראוי זה להיות שופט:

Thus, he does not think viyduim binds to leshivteichem, as a matter of syntax. Even so, I {=Josh} would note that his interpretation of the meaning of the lexical item by itself is fairly close to the midrash as found in Sifrei and Rashi -- that they are known (to those who would know them, and obviously appoint them) to be of the caliber to be a shofet.

However, the parse that Rashi offered because of the Sifrei is against the trup. That trup is:

The reason it is against the trup is that the first dichotomy within the phrase ending leshivteichem is at viyduim. Thus, anashim chachamim unvonim are all one entity, and all of these are chosen leshivteichem. If we would want to put viyduim together with leshivteichem, perhaps we should have to move the trup symbol one word earlier, and join the two words by putting a mercha under viyduim. Or even if we would put a zakef rather than tevir under unvonim, it would then be the first dichotomy, and then we could place a tipcha under viyduim as it now stands, but for musical rather than syntactic purposes.

I'll close by noting that much, though not all, of this post came from Mendelsohnn's commentary.