Smoke out of carb

Well, you probably are not far off with the eyeballing; the retarded timing with such chain wear would not make the car not run or hard to start per se, but it would offer more opportunity for the chain to jump timing. 'One valve out of spec' is hard to interpret; do you mean the lash was not in spec? If so, was it far out of spec?

But if the car runs OK for a couple of miles, then it sounds like a valve sticking or a fuel issue. When the car runs good, is it reasonably smooth and powerful? How old is the car, did it sit for a long time before you got it, was the tank flushed, etc.?

Run the compression check as suggested; it will not hurt to know, and if one is low, then you will know where to look. And if you do a leak down test, be aware that there will be SOME air leakage past the rings; a slight hiss is normally not a casue for alarm. A compression test is better at this point IMO, as it gives you some quantifiable info; makes sure the spark plugs are all out, and the throttle is held wide open.