Thank you for the beautiful elaboration on the subject of making a kinyan on Shabbos, and the difference between land or object and between dvar mitzvah or not.
On that subject, I recall a Tshuva of Rabbi Akivah Eiger to his brother where Rabbi Akiva Eiger uses the Sugya of the Kohen Gadol who prepares a second wife before Yom Kipur in case his wife dies to show that one cannot effect a kinyan on Shabbos even if the act of kinyan was done before Shabos. At the end, Rabbi Akiva Eiger brings a proof to his psak that even if one makes the maasei kinyan before shabbos he cannot have the chalos kinyan on Shabbos, from the Remo who paskens that if the pidyon haben date falls on Shabos , he should do the maasei Pidyon Haben after Shabbos ( although he could have done the maasei kinyan before Shabbos with a condition that it becomes effective on Shabbos) . Here we see that even for a dvar mitzvah , and even not for land purchase the Rema forbids a chalos kinyan on Shabos.
Thank you, too, for the clear summary of the Teshuvah of Rebbi Akiva Eiger.
When we wrote that a Kinyan is permitted on Shabbos for a Devar Mitzvah (based on the Magen Avraham), we wrote that it is only permitted for the needs of Shabbos and not for any other Mitzvah (such as Nisu'in and Pidyon ha'Ben). The logic is that only for a need of Shabbos is it permitted to do an Isur Shabbos, since it is being done for the sake of Shabbos itself. This is consistent with the Rema that you mention.
Be well, Mordecai and the Kollel