Recently, James Lamb posted a YouTube video on his channel that proposes an additional means to compute best focus using the number of stars detected. Since SGP has issues in auto-focusing SCTs or scopes with central obstructions, James did a detailed analysis comparing HFR with number of stars detected during an autofocus run. The number of stars detected correlates with the HFR, but using the number of stars detected seems to be more sensitive and robust to find the optimal focuser position for an SCT.
The other improvement to the autofocus routine would be to add a hyperbolic curve fit and perhaps use it along with the parabolic fit to determine optimal focus.
I continue to struggle with obtaining a good autofocus result with my Celestron 9.25" Edge HD, unless seeing is above average, even with a 0.7x focal reducer. SCT’s with long focal length are a challenge for the autofocus routine. For my scope, I am constrained in the number of steps used for each focus point where donuts will appear and a V-shape curve with a 3x step range is almost impossible for me to achieve without dog ears appearing. I do see that the number of stars detected increases significantly as the scope nears its best focus.