Is it the predator with the egr function(ver2.02)? If so make sure you have the egr turned off and if it still dose it add a egr blocker plate, that should fix it! THe added boost that ver 2.02 adds can in some cases push the egr pintle open and cause the turbo to bark with the sudden lose of exhaust drive pressure!
I asked because I did some research on this about a year ago. The EGR blocking did nothing for me either. What I have discovered, is that there is too much resistance in the factory LLY boost tubes, in combination with a stiffer air "spring" from the lower system volume, when running increased boost settings with tuners.
IOW there is too much backpressure on the compressor, and when the defuel occurs, boost demand is suddenly reduced, and the airflow in the induction tract wants to suddenly back up, reverse, into the compressor. This leaves the face of the compressor blades in a stalled condtion until the engine swallows the air that remains in the system (tubes and CAC). It is called compressor stall actually, and is very stressful to the blades.
there is no question that boost tuning will increase sensitivity to bark. On extreme tunes especially.
Now the question, is where to find improvement. Just addressing this as any engineer would address the cause of the compressor stall. There is only 2 main ways to induce it. Add pressure to the compressor discharge (like undersized boost tubes), or decrease pressure on the intake box side of things.
Perhaps the quickest test, is just remove your element, and try to reproduce the bark. Is it as severe? If removing the element makes a substantial change then that is one area to address. Don't worry, driving a mile with no element won't hurt a thing. Just don't get in back of a dirt hauler