I have tried reducing the output inductor value and this eliminates the oscillation problem into full load. However, the output switching noise is much higher (on the order of 400 mV p-p with Lout = 2.2 uH where the original value was <100 mV p-p with Lout = 4.7 uH). Also, I have not seen significant reduction in the amount of transient droop when I reduce the Lout value and increase the Cout value.
I will try removing R155 to determine if the LMP8646 is contributing to both issues.