"Effectively building a larger tunnel and then lining it afterwards"


Yep. The vertical shaft in the Meidum pyramid (leading to the burial chamber) shows tile-work, albeit thin and obvious. I wanted to visually re-visit this shaft (Waggy had a great write up on the pyramid a while back Meidum Pyramid page 31) because the vertical grooves and beam supports are reminiscent of the AC's configuration. At meidum it seems as if the grooves were used to facilitate vertical lift. Likewise, there are support beams with concave tops similar to the ones in the AC although these still have wooden beams affixed.