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1) Using the TPS92662 would work, it has enough channels to bypass each LED. When shunting two you just command the two channels to shunt.
2) If there is an output capacitor it cannot change voltage instantaneously. In switched matrix LEDs the capacitors cannot be large. It can also be hitting OCP because the compensation has to change quickly for stepped output voltages.
3) TPS92515 and TPS92518 are much better for this since they are hysteretic but they are buck converters. it would need a supply rail higher than the LED stack.