Well, the idea of HFR etc. is that it is normalized to max/total intensity, which takes care of different star intensities. Strong deviations there should only happen if stars saturate, and that should usually not happen for many of them.
Don't mess up star sizes with what you see on screen - those are basically 'cut' at a fixed absolute intensity, and therefore apparent star sizes do seem to vary a lot...

Other issues can be that the range you scan is too large, and you start seeing pupil shapes in the far-from-focus parts. Depending on your optics, that can largely irritate the detection algorithms.

My experience with linear is that you definitely want to start quite close to focus, and don't go too far out. To ensure that, I usually pre-focus the very first filter of the day manually (usually with video mode on a bright star), and then apply filter offsets at filter changes before running AF (I do that on any filter change, i.e., every 1-3 hours or so. Also refocus-on-temperature and/or regular refocus (time-based) might help.

The only thing that really upsets my focus curves is seeing. If that is bad, or - even worse - highly variable, you likely have to increase exposure time and/or average several measurements per focus setting.

My 2¢

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