Shofetim: How does לִשְׁבָטֶיךָ bind?

Though he may later retract from this position, here is an interesting Shadal on parshat Shoftim involving Rashi, deviating from trup, and a unique reading into a pasuk.

The pasuk states

יח שֹׁפְטִים וְשֹׁטְרִים, תִּתֶּן-לְךָ בְּכָל-שְׁעָרֶיךָ, אֲשֶׁר ה אֱלֹהֶיךָ נֹתֵן לְךָ, לִשְׁבָטֶיךָ; וְשָׁפְטוּ אֶת-הָעָם, מִשְׁפַּט-צֶדֶק.

18 Judges and officers shalt thou make thee in all thy gates, which the LORD thy God giveth thee, tribe by tribe; and they shall judge the people with righteous judgment.

and Shadal writes:

לשבטיך : מוסב על תתן לך ( רש"י ) , והיא נגד הטעמים , ועם כל זה נכון הוא בעיני , והכוונה שהשופטים והשוטרים יהיו מאותו שבט , כי יקשה בעיני הממון להיות משועבדים לאנשים שהם משבט אחר

The trup reads:

שֹֽׁפְטִ֣ים וְשֹֽׁטְרִ֗ים תִּֽתֶּן־לְךָ֙ בְּכָל־שְׁעָרֶ֔יךָ אֲשֶׁ֨ר יְהוָ֧ה אֱלֹהֶ֛יךָ נֹתֵ֥ן לְךָ֖ לִשְׁבָטֶ֑יךָ

Which means that the division in terms of trup is:
שֹׁפְטִים וְשֹׁטְרִים, תִּתֶּן-לְךָ בְּכָל-שְׁעָרֶיךָ, אֲשֶׁר ה אֱלֹהֶיךָ נֹתֵן לְךָ, לִשְׁבָטֶיךָ
becomes:
שֹׁפְטִים וְשֹׁטְרִים, תִּתֶּן-לְךָ בְּכָל-שְׁעָרֶיךָ,
אֲשֶׁר ה אֱלֹהֶיךָ נֹתֵן לְךָ, לִשְׁבָטֶיךָ

I think that this would mean that the shearim were given by Hashem to all the various tribes. And in each of these shearim you have a command to appoint shofetim and shoterim.

In contrast, if we would have a division like
שֹׁפְטִים וְשֹׁטְרִים, תִּתֶּן-לְךָ בְּכָל-שְׁעָרֶיךָ, אֲשֶׁר ה אֱלֹהֶיךָ נֹתֵן לְךָ, לִשְׁבָטֶיךָ
becomes
שֹׁפְטִים וְשֹׁטְרִים, תִּתֶּן-לְךָ בְּכָל-שְׁעָרֶיךָ, אֲשֶׁר ה אֱלֹהֶיךָ נֹתֵן לְךָ
לִשְׁבָטֶיךָ

then the command to place shoftim and shotrim is in accordance with your tribes, which Shadal at this point interprets as because people would not like someone from another shevet judging them.

Rashi notes this application, but does not make the same diyuk as Shadal.

for your tribes [This phrase] refers back to “You shall set up… for yourself.” Thus, the understanding of the verse is “You shall set up judges and law-enforcement officials for yourself, for your tribes, in all your cities that the Lord, your God, is giving you.”

for your tribes This teaches us that judges must be appointed for every tribe, and for every city. — [Sifrei, San. 16b]