@dmsummers, I'm theorizing only, but given the data you presented, I'm going to bet on refraction being your main residual driver below 40 degrees elevation angle. My logic is as follows: 1. The focuser is mainly using HFR, which is a measure of the size of the circle encompassing the star in the image. 2. Refraction directly effects the measured size of the circle, mainly beginning at 40 degrees above the visual horizon, as illustrated below:


3. Changes in the HFR outside the expected due to step movement show up as residuals (error) in the measured HFR, forcing the measured points to fall outside the polynomial used to determine best focus.
4. Temperature, pressure, humidity. dust, in the air volume the light passes through, all change the refraction of received light

What I don't know, is the size of the HFR errors produced by refraction at 40 degrees and below, or their stability, or the extent to which the programmer factored it into to the focuser tools, but given the parameters you've listed, I'd be surprised if it wasn't the main driver.