do a compression check and a vacuum check. Given your description, there could be many things going on. These checks will give information that helps narrow it down.
For example, a vacuum leak in the intake manifold gasket at the port to #1 and #2, could have been compensated for by enriching the fuel mix, causing 3 and 4 to run rich. OTOH, oil burning in 3 and 4 could be causing the plugs to soot up. Is the soot dry or wet? Wet is oil, dry is fuel.
31 Flamingos questions about timing and GAV setting are very pertinent. We need to know that information too. Check the point gap at each cam lobe. Some repro cams were ground incorrectly, and you'll never get it to run right with them. If there is play in the top plate of the distributor, the point gap will vary with the advance setting. A bad condenser can cause symptoms like these too, although its usually accompanied by backfiring. What is a "new" carburetor? Zenith? Tilly? is it new or rebuilt? if rebuilt, who rebuilt it?
