That's just the problem, white/gray doesn't clearly point at anything. Oil smoke is normally blue, but sometimes comes out a lighter color; steam (water) is generally pure white. Fuel smoke is normally black, but might be white if one (or more) cylinders is not firing at all (which would explain the put-put sound).
What happens if you remove the air filter, and watch the carb pistons as you rev the engine up? Does it run smoothly then? Do the carb pistons rise together?
The main advantage of vacuum timing, IMO, is that it does not rely on timing marks (which may be inaccurate).
Some other points to consider :
Occam's Razor only says "usually", meaning the problem may not be related (or related only indirectly) to the work you've just done. Carbon-core ignition wires are particularly suspect in this regard, since flexing is what kills them, and you have to flex them to R&R the head.
All of the high tension components (cap, coil, rotor, wires, plugs) can fail without any visible indication. I have seen a brand new Triumph rotor fail within an hour of being installed ... and the rotor was NOT defective when it was installed. It still looked brand new, but was leaking enough spark to ground to keep the engine from running at all. In that case, the root cause was a bad plug wire, plus a Lucas Sports coil that would put out more voltage than a stock rotor can handle.
My point is not that your problem is necessarily ignition; only that it's time to start actually troubleshooting rather than guessing.