Hello, it appears that with external mode the processor (highest frequency ISR) is being pushed to the limit and you are running into task overrun issues. See Higher PWM switching frequency in TI auto Code generation - #2 by Bryan_Lieblick for a detail explanation
One thing you could try is to divide down the highest frequency task - this can be changed in the initialization parameter by adjusting the parameter “trigger_divider”. For the 28379 it is set to 3. Try with the trigger divider set to 4.
This will change your control task execution rate from ~66.66kHz to 50kHz and with that reduction you might get the additional time needed to service the overhead added by the external mode.