What's the significance of בי״ה שמ״ו סימן, espcially on Dt. 31:28?

Question

In most sifre Tora (Torah scrolls), 240 columns of text each start with the letter vav (ו), and five do not. The first of those five exceptional columns, of course, is the first column of the Torah, which starts with a bes (ב); the other four start with the letters י (B'reshis 49:8), ה (Sh'mos 14:28), ש (disputed location; see e.g. Minchas Shay to Vayikra 18:8), and מ (also disputed; see e.g. Minchas Shay to Bamidbar 24:5).

At each of the exceptions, there's a masoretic note (duplicated in most print chumashim) that indicates the anomalous column with the phrase "בי״ה שמ״ו סימן",‎ "'בי״ה שמ״ו' is a mnemonic device". Indeed, that's a nice mnemonic, and the phrase comes from T'hilim 68:5.

But it's clearly not meant as only a mnemonic device because — and here's the kicker — a specific column is designated as the vav of that acronym. That same note appears on the word "וְאָעִידָה" (D'varim 31:28), which is at the head of a column.

So what's the deal? Specifically:

• Why is this acronym important, beyond serving as a mnemonic device? (After all, the designation of a specific column as the vav indicates that there's more to it than merely serving as a mnemonic.)
• Why are those six words at the heads of the anomalous columns; or, why are those six columns the anomalous ones? Especially, why is "וְאָעִידָה" listed as the sixth of the lot?

Answer 1

From what I understand, your second question is based on the assumption that every column begins what a Vav.

While this seems to be common practice, it is frowned upon by the Poskim who seem to claim that it has no basis in halacha.

See for example the Keseth HaSofer at the end of Ch. 4 - and the footnote there. He claims that the ווי העמודים - as it's commonly called - causes Sofrim to expand and shrink letters at will - ברצותו מרחיב יברציתו מקצר - in order to achieve this effect, and should be abolished.

He also Paskens that a Sefer Torah is Kosher without conforming to this convention of בי״ה שמ״ו.

Answer 2

Not all columns do start with vav, not all columns must start with vav, and the custom to make all of them start that way became far more popular some 30 years ago according to http://lavlor.blogspot.co.uk/2013/08/how-many-lines-should-my-torah-scroll.html (H/T to Zvi's accepted answer on the linked question). Before Davidovich's tikkun, I understand the practice was to begin columns (other than the 6 specific columns) with any of the 6 letters from the mnemonic. The 6 noted columns obviously had to begin with those specific words (One couldn't for example write מה טבו אהלך on the last line of a column and begin with יעקב to start the column).

Rav Yaakov Kaminetsky in his Emet L'Yaakov notes that many of the examples from the mnemonic are to accomplish other things. The bet of בראשית is obvious, and both the ו here and the ה are so that the songs which follow begin the desired amount of space down the column. I believe this discussion is right at the start of Emet L'Yaakov, but am not positive this minute.

I believe Rambam in Hilchot Sefer Torah, Tefillin u'Mezuzot Chapter 8 says how far down the column Haazinu should be, but again I am having trouble finding it just now.