Poor Buck Converter Current Limiting?
I don't see a problem with your proposal - if you take care of ceratain side conditions: The current limit does not appear to be low-pass filtered inside the chip, so it is not primarily about continous output current, but about monentary inductor current. This means that the amplifier for the high-side current has to be fast enough to terminate the pulse if the current starts to rise above the set limit. This is especially important if the current limit is set near the saturation current of the coil.

The oscillator frequency of the chip is 150kHz. If you declare a 1% widening of the duty cycle acceptable, the maximum allowed delay introduced by the current sense amplifier you are adding is 1/15µs, i.e. 60ns. If you don't get the current sense amplifier that fast, you can counter it by setting a lower threshold to get more time for turn-off. Keep in mind that the current rise speed is proportional to the input voltage, though.

Also, you should make sure that the current amplifier is operational during power-up, as current limiting is needed especially on the first cycles, when there is no feedback signal yet.