Was Hakhel performed in separation of men and women?

Question

Mitzvat Hakhel requires the presence of men, women, and children in the Azara (135x135 Ama incl. 4 Lishachot), with a tremendous density (for 600K grown-up men it's around 4M people per 4,000 sq.m.), as the Mishnah in Avot testifies "עמדו צפופים" and a Torah portion (Kodesh) is read in public.

The only separation of men and women in the Azara in the Temple I recall is mentioned in Mishnah Midos 2,5 and Succah 51b and, seemingly, was only instituted in the Second Temple^{source needed}:

מאי תיקון גדול? אמר ר' אלעזר כאותה ששנינו (משנה מידות ב, ה): חלקה היתה בראשונה והקיפוה גזוזטרא, והתקינו שיהיו נשים יושבות מלמעלה ואנשים מלמטה.

Is such a separation mentioned anywhere about Hakhel?

Answer 1

Rabbi Uri Sherqi says (starting at 36:30) that we don't find any sources mentioning a separation of men and women during הקהל:

פלא הוא שהיה במקדש מעמד אחר שבו היו יותר גברים ונשים מאשר בשמחת בית השואבה ושם לא הייתה מחיצה: בהקהל. במעמד הקהל פעם בשבע שנים באו כל ישראל אל בית המקדש - גברים ונשים וטף - ולא הייתה מחיצה

It is a wonder that there was an [lit. another] event in the מקדש in which there were more men and women than in שמחת בית השואבה and in which there was no partition: in הקהל. During הקהל, once every seven years, all of Israel came to the מקדש - men, women and children - and there was no partition.

Rabbi Sherqi offers an explanation as to why that is the case for הקהל as opposed to שמחת בית השואבה when men and women were in separate areas.