I had the same problem on my 1965 Mustang, but it was #5 cylinder that would foul. But same exact symptoms. I found out that the valve stem seals were shot. New ones are soft, the ones I took off were rock hard. You "should" be able to take off the valve cover and poke at the little black seal between the valve spring. If it is flexible, then start looking at the rings, etc.
I replaced the seals with the head on the engine in the car. Long story short: use compressed air to hold the valves up, buy or rent a one sided valve spring compressor, use the handle of a large screw driver to loosen the keepers from the retainer, and keep a magnet handy to pick up the keepers.
tanx,
Mugsy