"Thinking outside the box, sometimes brake boosters can develop vacuum leaks that are only exposed under hard braking, and then your engine would be sucking air brake booster vacuum line, and would run lean and could stall."

Found this in a post for a different car, but this is what I had been thinking was my problem.. with the hard peddle after accelerating, car dying if i pump brake, hesitation... SO gunna change that booster if this center diff isnt my issue... but how do i check my center diff??

If im in neutral rolling, does the transfer case still fully function? so i can cross that off the list? or does it some way some how disengage itself?