Oil pump won't cause a puff of smoke unless it has stopped pumping or is bypassing and that is "not pumping". Only then will you see this elusive puff of smoke. When you tore it down, you'd also have seen a bad crankshaft, rod, cylinder walls, piston skirts and rings, not to mention the valves and guides would also be galded.
If you break the ceramic out of a spark plug, take an air tool adapter and put it into the broken spark plug and weld it together. Screw the new tool into the spark plug hole, place the air hose on it and that will spin the engine down to bottom dead center on that cylinder. Remove the valve spring retainer locks, then remove the springs. Check to see if you can wiggle the valve inside the guide. If it is really noticeable, you need to either replace the valve guide or valve or both. This is the time to replace the valve stem / guide seals regardless of the wear factor of your guides and valves.
Even if you're going to purchase the cheap, cheap, cheap heads, before you remove the current heads, replace the seals and see if your puff is gone.
The oil pressure switch may have gotten cracked and causing the oil pressure fluctuating if the oil pressure is about 40 to 65 pounds with a manual gauge at 3000 RPM. Beg, borrow or steal (ok, don't steal) a manual oil pressure gauge and check the pressure before you worry about doing the valve seals and guide/stem check.
You'll find the problem eventually,
Good luck,
Max