As you are using SGP v4 you have a new option to use ASTAP for detecting and measuring stars during autofocus. I think it is by far the best option but you can experiment for yourself - choose a night when the moon is near full and no good for imaging. As noted above on the AF focus curve this option shows HFD rather than HFR.
If you have the time and endurance to read it all, much of the background leading to the provision of this option is contained in this thread:
You may already be using ASTAP for platesolving (it is very quick) but if not you will need to download and install from here.
Once you are up and running with SGP AF there is not a great deal you can do to fine-tune it apart from:
a) Vary the step-size and/or number of steps. You need to select values that will get you reasonably out of focus (3-5 times your best obtainable HFR) while still giving you (I suggest > 5 star detections) at the extremities. With an L filte this is generally not an issue but can be more of a challenge using NB filters. For what its worth, with my f/6 refractor I use 7 x 60 steps with exposures varying from 5 - 30 seconds at 2x2 binning.
b) Atthough SGP currently uses a parabolic curve fit the actual curve should be hyperbolic so if the outermost data points with a typical 7 step AF run are not in moreorless a straight line you may have uncorrected backlash, a poor choice of step-size or poor observing conditions on the night.
c) If you start an AF run with your scope close to best focus for the conditions then you should get a nearly symetrical AF curve. An issue with the current parabolic curve fit is that it can give a poor result if the AF curve is greatly extended on one side or the other. You can guard against this to a degree by setting a more demanding AF quality fit increasing the custom variable ‘quadratic_fit_min_quality’ to say 0.98.
d) Once you are reasonably confident in your AF set-up then if you think there maybe benefits then you can start looking at filter off-sets and temperature compensation.
And, going back to your original question, while focus accuracy is a key determinant of HFR, other factors such as tracking accuracy, seeing and temperature stability can also will have an impact.