I don't think it was Gregory, I think it was more likely the mimic using recording of Gregory's voice to guide Cassie into a place where it could corner her- Why Gregory wouldn't tell her to unlock the scooping room and go to it instead of going to the elevator.
It certainly makes more sense than Gregory having remote access to the pizzaplex. Also with Gregory's final words to Cassie before the elevator drops and leaves her severely injured, I think that was also the mimic, gloating over luring Cassie down and then finishing her off.