On Shabbat Hagadol, the Sabbath preceding Pesach, it's customary to review the region of the Hagada starting from "We were slaves" (after The Four Questions) and ending with "to atone for all of our sins" (at the end of the Dayeinu wrap-up). Why that section, and not the parts before and after?
Yaakov Emden was also not so happy with this מנהג, giving the same reason mentioned by the Vilna Gaon (that it says in the Haggadah "only when there is Matzah and Maror in front of you"). He also gave another reason, that reciting the הגדה before the סדר, was akin to eating מצה on ערב פסח. (He was thus more concerned with the מנהג when פסח lands on a Sunday, and ערב פסח is שבת.)
However, the text of רבן גמליאל is required to fulfill one's obligation. But the portion of the הגדה recited on שבת הגדול ends right before רבן גמליאל. Thus the text has no pretension of the מצוה that is exclusive to the סדר night, and thus we can avoid the concerns of the גר"א and יעב"ץ.
I suppose מה נשתנה is not included because it makes little sense to ask about rituals that have not be done yet. הא לחמא עניא is similarly out of context when recited away from the סדר table.