A simple method of avoiding shoot-through here, is not to use the
synchronous rectifier. Replace the bottom fet with a schottky diode.

Synchronous rectification has it's place.
Predictive gate drive of a synchronous rectifier has its place.
Integrated comntrollers have their place.

What you probably need here is a simple buck regulator that will
cycle-skip below a certain duty cycle.

OV or zero current are both difficult ("undefined") conditions to
'regulate', unless there's a means to reduce or reverse stored energy
in the inductor during the free-wheeling period.

Synchronous rectification handles the zero-current condition nicely. A
minimum or switched internal load will serve otherwise. For zero
voltage, a nice freewheeling voltage loss comes in handy in the
absence of a negative supply, but cannot be counted on to actually
reverse energy flow in each cycle - so there's still a minimum current
under which zero output volts can be regulated. The lower the voltage,
the higher this current will be.

Cycle skipping will occur naturally in most (all?) single-quadrant
regulators around the "undefined" operating conditions. This is
naturally chaotic, but generally benign and is useful in stretching
out performance extremes. However it likely unsuited to any
'predictive' technique. Perhaps that is what is actually being seen
here.

RL