Now, there are obviously inaccuracies in the tracking of the Sun, Moon and nodes using this method. The solar year isn't 364 days long, nor is the lunar synodic month 28 days. However, these can be corrected periodically through various methods suggested both by Hawkins and Hoyle.
The most obvious correction is that the Sun should be placed in AH28 at winter solstice every year, and AH56 at summer solstice - if it isn't already in the correct hole (it'll be a one-hole move).
The Moon can be corrected monthly, to place it directly opposite the Sun marker at full moon.
The node positions can be corrected any time an eclipse is viewed that wasn't "predicted" ahead of time (probably just after the priest has been sacrificed).
My purpose here is to demonstrate how 56 holes can be used to track the positions with reasonable precision over time, I am specifically NOT arguing that this is definitely what the AH circle was used for.