Jewish Commemorations on Specific Days of the Week

In my last post, I proposed that Yom Haatzmaut should always be celebrated (but not observed) on the first Thursday after 1 Iyar (I formulated it a bit differently, but BZ streamlined it). I mentioned that I don't know of other instances where a Jewish commemoration takes place on a particular day of the week, coordinated with a date. In fact, there are several examples, though some are pretty far-fetched:

• The best example is the manner in which Purim was observed by villagers in Mishnaic times (see m Megillah 1:1-2). They would always hear Megillat Esther on a Monday or Thursday, either prior to or coinciding with 14 Adar. If I recall correctly, they would still hold the festive meal and deliver mishloach manot on the 14th. The reasons for this maneuvering were socioeconomic, though they found scriptural license ('zmaneihem'). This would be a perfect parallel if not for the fact that, in it, the liturgical components were shifted (except for al hanisim, if they said it; matanot le-evyonim were bound to the reading of the Megillah), whereas the celebratory components remained constant. Nevertheless, I see no reason why liturgy would be more flexible than a meal a priori.
• According to Ashkenazic custom, we begin saying selihot on the last Saturday night before the last Wednesday before Rosh Hashana (think about that definition; it works).
  
• The customary fast days of BeHa"B fall out on the first Monday-Thursday-Monday set after 1 Iyar (and often coincide with Yom Haatzmaut! I believe that at Mercaz HaRav, they say both Hallel and Selichot in the same service when that happens. Talk about an emotional roller-coaster!).
• The "dalet parshiyot" are recited on Shabbatot which correlate to calender events (the beginning of the months of Adar and Nisan, and Purim).
  
• Finally, going a bit further afield, the day of Hakravat Ha-omer was the first Sunday after the beginning of Pesach according to the Sadducees (I had to throw that in).