Sounds like you might be leaking coolant into the cylinder after a drive. Then there might be enough liquid in the cylinder to dead head at the next startup. Dead heading will produce a whack and then the liquid is expelled on the next exhaust cycle. Then there would be a miss until the spark plug dries out. It might explain all of the symptoms you are describing. Including the white smoke while it is running. In the case where the whack is not heard and the miss is there for 30 seconds, it is conceivable that the offending cylinder is in an exhaust cycle and the dead head does not occur but the plug still gets wet. I would suspect a head gasket. If the whack is consistent, then I would remove all the spark plugs and crank the engine and see if you get any coolant blowing out the plug hole. That would be obviously where the problem is.
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I have to agree with your opinion. Makes all the sense in the world.

My question is what makes the whack sound. Obviously when the cylinder fires the explosion that occurs creates the sound. But it doesn't always make the noise when I get the smoke. This probably has to do with how far the cylinder is up or down at the time the car stops? Correct?

Head Gasket issues generally derive from overheating which warps the head and causes the gasket to seperate producing the coolant leak. I will assume that I have one or more cylinder leaks (probably one, thats why the thwack is so random). At any rate I'm looking at a new head or machining the old head.

Many, many thanks for taking the time to respond. Last question would be: This seems to be something that a seasoned mechanic would know. I wonder why my guy didn't suspect or know about the deadheading? If he knew why would he avoid the obvious head gasket problem? Makes me a little leery! Should I be?

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1988 560SL
Black Pearl/Palamino