I found explanations in Rite and Reason: 1050 Jewish Customs and Their Sources By Shemuʼel Pinḥas Gelbard (p. 129). I am summarizing:
The 1st answer mentions that the Torah should be raised slightly at the name of Hashem (God) in each of the 3 verses, Shema, Echad Elokeinu and Gadlu. This is because we want to elevate God's name. (My opinion - this answer only seems to explain why we do this for "Gadlu" as the word Gadlu means "make big" or "elevate". I haven't seen the raising done for the other 2 verses.)
The 2nd answer explains why the cantor faces the congregation for Shema and Echad Elokeinu but faces the ark for Gadlu. Two reasons are mentioned. The reason I think is stronger states that in "Gadlu" the cantor includes the word "iti" - "with me", so he faces the ark to symbolize that he includes himself.