The central source for the shalosh shevuos is the aggadic passage in Ketubot, which Peninei Halakhah, Zemanim 4:4 quotes as teaching that the Holy One adjured Israel not to ascend the wall, not to rebel against the nations, and adjured the nations not to oppress Israel excessively — and that Rabbi Elazar warned that violating the oath would forfeit divine protection.
Avnei Nezer, Yoreh Deah 454 takes up the question of settling Eretz Yisroel in the present era and directly grapples with those aggadic passages, including the verse 'השבעתי אתכם' (Shir HaShirim), acknowledging that the matter is exceedingly difficult to resolve since it turns on aggadic sources in the Gemara and Midrash Shir HaShirim whose true meaning the sages deliberately concealed, and that the halachic question depends entirely on how that aggadah is understood.
The passage at Avnei Nezer, Yoreh Deah 454 then turns to the Gemara's discussion of Rabbi Zeira evading Rav Yehudah's company because he wished to ascend to Eretz Yisroel — given Rav Yehudah's position that one who goes up from Babylonia to Eretz Yisroel transgresses a positive commandment — indicating that the Avnei Nezer's analysis of the shevuos is conducted in Yoreh Deah 454, not in 461.
Avnei Nezer, Yoreh Deah 461 opens with a letter dated Iyar 5639 addressed to his father-in-law on the laws of nidui and cherem, and its passage gives no indication of treating the shalosh shevuos or the question of conquest of Eretz Yisroel before the coming of Moshiach.
Mishneh Torah, Melachim and Wars 5:1 classifies the wars a king may initiate — mandatory wars (milchemet mitzvah) against the seven nations, Amalek, and in defense of Israel, and discretionary wars to expand Israel's borders — but makes no reference to the shalosh shevuos or to any prohibition on conquest tied to a pre-messianic era.
Tzitz Eliezer 10:1 engages with the Avnei Nezer's rulings concerning the sanctity of conquered territories in Eretz Yisroel and their obligations in terumot and ma'aserot, analyzing how conquest relates to the revival of the land's original sanctity for Torah commandments dependent on possession of the land, rather than addressing the shalosh shevuos directly.