I've played a bit with dead time and minimum pulse width.
When I reduced the dead time near very low and very large pulses (but not to large, ie 96-98% of Dmax), the distortions at zero cross were smaller. Also when I put the limit to min pulse value, the distortion were smaller. With outsynchronizing LF leg the glitch disappeared but oscillations were bigger.
The effect was similar to that in this app note from TI "How to Reduce Current Spikes at AC Zero-crossing for Totem-pole PFC" . The modulation for this PFC is the same.
Moreover they completely removed the spike around zero and oscillations! Looks like I was close to achieve that.
https://www.ti.com/lit/slyt650I will adopt that algorithm to see the effects.
My LF MOSFETs have also fast recovery diodes and fairly small output capacitance so it should be easier to achieve that.