Unless the muffler is restricted inside causing back pressure it will not be causing the problem you describe. You mention the car has been prone to overheating, that concerns me, perhaps the head gasket is blown or mildly blown. I have seen the intake manifold gasket fail causing a vacuum leak, it could be a multitude of things very hard to guess at without being able to drive the car and experience the problem firsthand. Does the engine idle smoothly or does the idle feel rough? Is the "choking and faltering " experienced at idle , mild acceleration or only under prolonged acceleration or under load?