This report from Australia does not give absolute degree of movement, but suggests that it is more than has been recorded for Polaris.This observer also notices the Figure 8 motion over the 24 hours period, based not only on the constellations but also the Moon and Sun.
Dec 22: Today observing Sigma Octantis. The position of Sigma Octantis on the evening of Dec 22 appears to suggest Earth is moved toward the setting Sun.
Dec 25 I'm glad, in a sense, that someone else is observing Polaris having moved. That there seems to be a difference in Polaris' movement and Sigma Octantis' movement is suggestive (to me) that there is a pivot point for sway not through Earth's equator, but higher, perhaps through the Earth at the 70° Nth parallel or lattitude. If true, this might explain why Polaris moves less than Sigma Octantis. I observed the near-Full Moon to be setting in the NW early this morning at 4:00 AM this Dec 25. And Sigma Octantis at 4:00 AM seemed to the right of my terrestrial target, suggesting Earth was moving to the left. When this happens the rising Sun often later appears southward.