I recommend going up and over Glingmans Dome for sure. Yes the AT is marked with white blazes. Super easy to follow. I don't know if it is practical but you could take two cars and park them at different spots so you don't have to back track or anything like that.
I was planning on going there. Is there any good overhangs? And is the an overhang that kind of shadows over the whole park? If not we're just gonna find the highest point and hike to it.