Tashlikh on Hoshana Rabah

The Jewish custom of tashlikh is recorded by Rabbi Mosheh Isserles (ReMA) in Shulhan Arukh, Orah Hayim, chpt. 583, paragraph 2. Speaking about Rosh ha-Shanah, ReMA says: “[people] go to the river to say the verse ‘and throw (ve-tashlikh) all our sins into the depths of the sea etc.’ (cf. Micah 7:19)”. Mishnah Berurah (ibid., note 8) codifies that tashlikh should be done on the first day of Rosh ha-Shanah after the minhah service but before sunset. Mishnah Berurah also records the custom that if the first day of Rosh ha-Shanah falls on Shabbat, tashlikh should be performed on the second day of Rosh ha-Shanah in order to avoid any danger of transgressing Shabbat by carrying in a public domain. The contemporary expert in Jewish law (posek) Rabbi Gavriel Zinner quotes sources that state that if someone was unable to perform tashlikh on Rosh ha-Shanah they are allowed to do it throughout the Ten Days of Repentance (aseret yeme teshuvah) – see: Sefer Nite Gavriel : hilkhot Rosh ha-Shanah [Yerushalayim : 2001], chpt.69, paragraphs 15-16 and footnotes 25-28, p.424. Furthermore, Rabbi Zinner quotes many sources that indicate a custom to specifically perform tashlikh on the same day of the aseret yeme teshuvah as the penitential prayers (selihot) contain the responsive liturgical poem (pizmon) which incorporates the Thirteen Attributes of Mercy (derived from Exodus 34:6-7) into its structure (either the fourth or fifth day of the aseret yeme teshuvah, depending on the year). Rabbi Betsalel Majersdorf, Technical Services Librarian at Jewish Theological Seminary, mentioned to me that he has recently become aware of a practice to specifically wait until after the aseret yeme teshuvah and recite tashlikh on the seventh day of Sukkot, Hoshanah Rabah. Rabbi Majersdorf was unaware of the source for this practice. I searched the literature but have also been unable to locate such a source. We would like to request that any readers of this blog who know of any sources on this matter please note them in the “comments” section. Thank you.