It is true that Rashi in Megilah does not mention that Sancheriv's army fell on the seventh night of Pesach. He seems to be saying that we read about Sancheriv on the seventh day of Pesach since Sancheriv fell on "the evening of Pesach," i.e. the first night of Pesach (while the Jewish People were eating their Korban Pesach), as you write. This is in fact consistent with what RASHI writes in Yeshayah 38: 1 and Melachim II 20:1, and with the words of the MIDRASH SHEMOS RABA 18:5, cited by the TORAS CHAYIM Sanhedrin 95a and paraphrased in the poem "va'Yehi ba'Chatzi ha'Laylah" (which is recited on the night of the first Seder).

If so, the Jewish people were not reciting a half-Hallel on the day of Sancheriv's fall, and the answer of the Rogatchover Gaon will not be viable.

However, RASHI in Yeshayah 9:2-3 and 30:32 cites another Midrash, which asserts that the fall of Sancheriv was on the second night of Pesach, during which the Omer barley is harvested. This is the way the TOSFOS YOM TOV quotes the Rashi in Megilah 31b (despite the fact that he references the Rashi in Yeshayah 38 which states otherwise).

This is in fact consistent with what our Gemara teaches, that Chizkiyah did not recite Hallel on the day that Sancheriv's army fell. This also seems to be the Gemara's intention (95b) when it teaches that the night of Sancheriv's fall was "when grain becomes ripe to harvest," i.e. it occurred on the night during which we harvest the first of the year's grain (the second night of Pesach, when the Ketziras ha'Omer takes place).

The Tzafnas Pane'ach apparently had in mind these citations from Rashi (i.e. that the army of Sancheriv fell on the second night of Pesach) when he wrote what he wrote. According to these Rashis, the explanation of the Rogatchover is indeed viable (even if the fall of Sancheriv did not occur on the seventh night, as we wrote in the Insights).

Best wishes,

M. Kornfeld