It is a broken valve spring!
 

The VW 1.8 uses a pair of valve springs -- I stripped the head and removed the camshaft and, at TDC for the misfiring #1 cylinder. Lo and behold, once I pulled the follower that covers the valve, I was able to push the valve down pretty easily. I tested it against all seven others and the #1 exhaust was by far much easier to push down.

Now I just need to figure out how to pull the collets and get to the springs. I don't have access to compressed air to hold the valve up, so maybe I just use the rope trick to hold the valve in place? Any suggestions much appreciated as I do not want to pull the head.

Anyway, the lazy exhaust valve would not stay shut at compression so I cannot imagine what sort of unburnt mixture has gone into the catalytic converter. Oh well, the car was free...

Many thanks for your help on this one, and a data point for folks I guess if they are experiencing misfiring.

John