I'm not so sure it's the IAC.When mine went, it would start idling high with no warning. Or, would idle so low it would stall out in D or R. Never in Park.
If your engine has a mis-fire, it sounds more like timing, spark or ignition.
How does the timing belt look? How is the tensioner and does the belt have any slack between the two cams? If yes, then here lies the problem.
