Should shatu have stress on the first or last syllable?

Last week Thursday, anon1 asked a question on parshas Behaalosecha that I was not able to research appropriately to answer intelligently off the cuff. He asked:

Probably too late for this year (though I would still read it next week) but any thoughts on the trop of the word SHOtu vs. shoTU (11:8). The minchas shai quotes both and I have hears some standard stuff on this but you always seem to have an interesting angle on these things. Thanks and good shabbos.

The pasuk in question is Bemidbar 11:8:

ח שָׁטוּ הָעָם וְלָקְטוּ וְטָחֲנוּ בָרֵחַיִם, אוֹ דָכוּ בַּמְּדֹכָה, וּבִשְּׁלוּ בַּפָּרוּר, וְעָשׂוּ אֹתוֹ עֻגוֹת; וְהָיָה טַעְמוֹ, כְּטַעַם לְשַׁד הַשָּׁמֶן.

8 The people went about, and gathered it, and ground it in mills, or beat it in mortars, and seethed it in pots, and made cakes of it; and the taste of it was as the taste of a cake baked with oil.

Is the first word in the pasuk pronounced with stress on the first or the second syllable? Before answering, perhaps we should see the Minchas Shai.

He records two different positions, one that it is milera, acknowledging that it would be weird, but gives examples (such as saru hatzefardeim, but more on this later, perhaps). Another suggests how this belief it is milera could have come about, though if it is tradition, so be it. The suggestion for why one would think it is milera is that the trup sign on it is a telisha ketana, which is always placed at the end of the word, in order to distinguish it from the telisha gedolah, such that it does not mark the place of stress. I would add that in some sefarim meduyakim, they would (and in this case do) put two telisha ketanas on the word, one in its regular place at the end of the word and one in the place of the stress, just as they do for pashta. {note: updated to more closely match what minchas shai actually says. see comment section.}

I asked Dr. David Segal about whether it should be shatu or shatu. He told me that he reads it mile'el, and when someone asked him why, he told him that "whoever says shatu aino eleh shoteh." The idea behind this is not just the pun, he explained to me. Rather, it gives the explanation. שטו can either be from the root שוט, which is a hollow root, or it could be from שטה. We know based on meaning in this pasuk that it is שוט, which means to roam. See Iyov 1:7, which shows it is שוט within this meaning:

ז וַיֹּאמֶר יְהוָה אֶל הַשָּׂטָן, מֵאַיִן תָּבֹא; וַיַּעַן הַשָּׂטָן אֶת יְהוָה, וַיֹּאמַר, מִשּׁוּט בָּאָרֶץ, וּמֵהִתְהַלֵּךְ בָּהּ.

7 And the LORD said unto Satan: 'Whence comest thou?' Then Satan answered the LORD, and said: 'From going to and fro in the earth, and from walking up and down in it.'

When it is a hollow root, it would be mile'el. For example, kamu, from קום. But if the root were שטה, which is the same as shoteh, then it would be milera. As such, this functions as a nice mnemonic and explanation as well.

I would also add that in the Etymological Dictionary of Biblical Hebrew (pg 257), based on Rav Shamshon ben Refael Hirsch, he gives gradational variants as שטט, scourge, שוט as roam, and שטה, deviate.

Dr. Sefal noted (without having seen the discussion in Minchas Shai) that there are exceptions, and it is interesting to try to explain them, perhaps midrashically. One example he gave was that in Minchas Shai, of saru hatzefardeim, where the root is סור and yet it is milera. Thus, in Shemot 8:7:

ז וְסָרוּ הַצְפַרְדְּעִים, מִמְּךָ וּמִבָּתֶּיךָ, וּמֵעֲבָדֶיךָ, וּמֵעַמֶּךָ: רַק בַּיְאֹר, תִּשָּׁאַרְנָה.

7 And the frogs shall depart from thee, and from thy houses, and from thy servants, and from thy people; they shall remain in the river only.'

As Ibn Ezra notes there:

וסרו -
באה זו המלה מלרע הפך המשפט, וכמוהו: כי שמו אותי בבור.

He gave over some explanations for what could spark this, and a possible pun in the commentary, but here is not the place.

One final note before I sign off on this. In the haftarah of this week's parsha, Shelach, Yehoshua sends spies from Shittim:

א וַיִּשְׁלַח יְהוֹשֻׁעַ-בִּן-נוּן מִן-הַשִּׁטִּים שְׁנַיִם-אֲנָשִׁים מְרַגְּלִים, חֶרֶשׁ לֵאמֹר, לְכוּ רְאוּ אֶת-הָאָרֶץ, וְאֶת-יְרִיחוֹ; וַיֵּלְכוּ וַיָּבֹאוּ בֵּית-אִשָּׁה זוֹנָה, וּשְׁמָהּ רָחָב--וַיִּשְׁכְּבוּ-שָׁמָּה.

1 And Joshua the son of Nun sent out of Shittim two spies secretly, saying: 'Go view the land, and Jericho.' And they went, and came into the house of a harlot whose name was Rahab, and lay there.

If, as we have seen from Iyov, שוט means to roam, and can be used by one exploring and noting what he sees, then perhaps this can be a basis of the place-name.