"כִּמְעַט שֶׁעָבַרְתִּי מֵהֶם עַד שֶׁמָּצָאתִי אֵת שֶׁאָהֲבָה נַפְשִׁי" (ג, ד)
The Vilna Gaon zt"l explains our pasuk to be alluding to the return of Ruach HaKodesh in the Midbar, which was after Yom Kippur. After the Eigel, B'nei Yisroel cried to Moshe to help them find atonement before Hashem. For the last forty days on Har Sinai, Moshe cried for them. From the first of Elul until the 10th of Tishrei. Finally, on day 40, Yom Kippur, Hashem forgave the B'nei Yisroel with His great mercy. ה' swore by the Kisei HaKavod that because they cried for forgiveness, the day of Yom Kippur would forever be celebrated as a day of "בֵּית שִׂמְחָה" - "Crying out of Joy." A day of atonement and forgiveness for all time. (לשון זהר, רעיא מהימנא פנחס)
The word כִּמְעַט alludes to ט' בְּתִשְׁרֵי, עֶרֶב יוֹם כִּפּוּר. The Vilna Gaon continues to explain that the love that B'nei Yisroel found as alluded to here in the pasuk, is the Second Luchos. They held on to the Torah, the word of their Beloved, never letting go... "אֵת שֶׁאָהֲבָה נַפְשִׁי" refers to שְׁנֵי לוּחוֹת הַבְּרִית.
The Medrash tells us that the mitzvah to build a Mishkan was given to B'nei Yisroel on the same day. Yom Kippur was a day of atonement, commitment to Torah, and bringing the Shechinah. (תנחומא) Here in Shir HaShirim, the Mishkan (as we learned above) is called "בֵּית אִמִּי" which stands for בֵּית ה' אֱלֹקֵי יִשְׂרָאֵל.
In this week's Parsha Hashem forgives B'nei Yisroel - "וַיֹּאמֶר ה' סָלַחְתִּי כִּדְבָרֶךָ" (במדבר יד, כ). This took place on Yom Kippur. (פרקי דרבי אליעזר) The gematria of "רֹאשׁ חֹדֶשׁ אֱלוּל ל-י' בְּתִשְׁרֵי - יוֹם כִּפּוּרִים" plus "וַיֹּאמֶר ה' סָלַחְתִּי כִּדְבָרֶךָ" equals 3,275, which is the same gematria as "כִּמְעַט שֶׁעָבַרְתִּי מֵהֶם עַד שֶׁמָּצָאתִי אֵת שֶׁאָהֲבָה נַפְשִׁי" (3,275).
