The parasha of Lot

I noted the following interesting dvar Torah on parashat Vayera at Avakesh:

אין לך שבת ושבת שלא יהא קורין בו פרשתו של לוט 

"There is not a Shabbos in which we do not read the parasha of Lot" Bereshis Rabbah 51:9 (see the commentary there Nezer HaKodesh)

There are those who say this midrash is a printer’s error since we only read the Parasha of Lot once a year on parshas Vayeira. However, the Munkatcher Rebbe (in Chaim V'Shalom) says... 

I am not really interested in kabbalistic or chassidic explanations, so I won't discuss the continuation, but the first part caught my eye. What is the meaning of this strange statement in Bereishit Rabba? And what is this printers error to which he refers?

The midrash in question reads:

ט. ותהרין שתי בנות לוט מאביהן אמר ר"א לעולם אין האשה מתעברת מביאה ראשונה אתיבין והא כתיב ותהרין שתי בנות לוט מאביהן אמר ר' תנחומא שלטו בעצמן והוציאו ערותן ונתעברו כמביאה שניה א"ר נחמן בר חנין כל מי שהוא להוט אחר בולמוס של עריות סוף שמאכילין אותו מבשרו רבי יודן דמן גלוי ורבי שמואל בר נחמן תרויהון אמרי משום רבי אליהועיני אין אנו יודעים אם לוט נתאוה לבנותיו אם בנותיו נתאוו לו מן מה דכתיב (משלי יח) לתאוה יבקש נפרד הוי לוט נתאוה לבנותיו ובנותיו לא נתאוו לו ר' תנחומא בר רבי חייא משם ר' הושעיא תורגמנא אין כל שבת ושבת שאין קורין בה פרשתו של לוט מאי טעמיה (שם) בכל תושיה יתגלע א"ר אחא יתגלעו אין כתיב כאן אלא יתגלע האנשים נתרחקו והנשים נתקרבו:

And the meforshim on Midrash Rabba can be read here. Matnot Kehunah explains that "Perhaps such was their custom in order to distance the nations from licentiousness..." Etz Yosef explains that "for then they were accustomed to read on every single Shabbat as well the parashah of Lot, to teach the nation how drunkenness brings about stumbling in sin. And from this, one who guards his soul will distance from this. However, there are those who are gores 'there is no year [שנה] in which they do not read ... [the parashah of Lot]', and it is a correct girsa." Then, in explaining the derivation from the pasuk in Mishlei, בכל תושיה יתגלע, he writes, "that is to say, on each Shabbat in which they read from the Torah which is called תושיה, then יתגלע, that is, the disgrace of Lot is revealed [=יתגלה, with a ה], for the [guttural] letters אהח"ה switch off."

I cannot entirely account for the meaning of the midrash. However, I would point out the following three points:

1) Emending שבת ושבת to שנה ושנה does not solve anything. This is Bereishit Rabba, which is the midrash aggadah material of the Amoraim of Eretz Yisrael. In Eretz Yisrael, they finished the Torah once every three years, not once every year. And so, they would not read Vayera every year. Furthermore, what would be the point of mentioning this an some novel chiddush. If we were to assume the Babylonian practice of completing the Torah every year, then every part of the entire Torah would be finished every year, so why single out this one parasha.

2) By parashah, they do not mean the sidra. A parasha just means a small section. It could, perhaps, refer to the approximately 1/3 of the sidra that they leined in a week in Eretz Yisrael. But it could also refer to a segment marked off by petucha and setuma gaps.

3) By שבת ושבת, this might means each week rather than each Saturday. After all, שבת also has this meaning. (See for one instance, of many, Ketubot 66b, 'each and every שבת'.) And so the reading of a particular day within the week would include the parashah of Lot. How so? This would then not (necessarily) be the typical Torah leining on Monday, Thursday, and Shabbos. Rather, there was a practice of the maamadot, where dedicated Yisraelim would read a specific portion of parashat Bereishit, and maaseh Bereishit, each day of the week. Thus, in the 4th perek of Taanit, in the Mishna:

וישראל שבאותו המשמר מתכנסין לעריהם וקורים במעשה בראשית.

ד,ג  ביום הראשון, "בראשית" (בראשית א,א) ו"יהי רקיע" (בראשית א,ו).  בשני, "יהי רקיע" ו"ייקוו המים" (בראשית א,ט).  בשלישי, "ייקוו המים" ו"יהי מאורות" (בראשית א,יד).  ברביעי, "יהי מאורות" ו"ישרצו המים" (בראשית א,כ).  בחמישי, "ישרצו המים" ו"תוצא הארץ" (בראשית א,כד).  בשישי, "תוצא הארץ" ו"ויכולו השמיים והארץ, וכל צבאם" (בראשית ב,א).  פרשה גדולה קורים אותה בשניים, וקטנה ביחיד--בשחרית ובמוסף; במנחה נכנסין וקורין על פיהם, כקורין את שמע.  ערב שבת במנחה, לא היו נכנסין, מפני כבוד השבת.

In this way, they sustained the world. (See Taanit 27b.) And they finished these sections of Bereishit each week. Perhaps as part of one of these readings of maamadot, there was a custom to incorporate the parashah of Lot on one of those days. Of course, I have no outside evidence of this. But the idea of an important ritual reading encompassed in a week's ritual reading would work well here. And we would not need to posit that a standard widespread practice in Eretz Yisrael through the time of the gemara was to take out a second sefer Torah each week and read a whole extra aliyah of the parashah of Lot, where there is no indication of this extra aliyah elsewhere in Talmud Yerushalmi.

Update: Imrei Yosher has an interesting idea that it should be שֶבֶת with a segol. Thus, every location, meaning each shul and beit midrash. And he cites another parallel text which talks about Lot's disgrace being learned in each bet knesset. And תושיה would be such a location. This sounds plausible, and does not even need a printer's error. I am not wholly convinced, though.