Ezra's takkanah to read Bechukosai before Shavuos

This Shabbos IY”H we will read the tochacha in Parshas Bechokosai. When we lived in Passaic, my Rebbe, R’ Yonasan Sacks shlit”a, would always point out on this Shabbos that this keriyas hatorah is not just a regular kiyum of reading parshas hashavua, but is a kiyum of a special takkana of Ezra (see Megillah 31b) to read the parsha of tochacha before Rosh haShana – Bechokosai is read before Azetert (Shavuos), which is called Rosh haShana for fruit of the tree, and the tochacha of Ki Tavo is read before Rosh haShana in Tishrei. (If I recall correctly, he would say to have kavanah to be yotzei the takanah through keriyas haTorah.) Even in the times of the Mishna when only the first and last oleh recited brachos on keriyas haTorah, there may have been a separate bracha on this keriya because of the takanah (see R’ Sacks’ article here ). Tosfos in Megilla points out that we do not want to read a parsha of kelalos just before a Yom Tov, so we intersprese Parshas BaMidbar in between the tochacha and Shavuos (see Tosfos with respect to the order of parshiyos in Tishrei). Food for thought: why is the tochacha read only before the “Rosh haShana” of Shavuos and not Pesach or Sukkot, which the Mishna also calls “Rosh[ei] haShana”?