Black Spark Plugs that Clean Themselves

Vehicle:

2002 Mazda Protégé LX, 2.0L engine, automatic transmission, 240,000 km

Recent Work:

Thermostat replacement

Symptoms:

• Owner reported that the car shook and stalled on startup. She parked
  the car and drove another vehicle.
• The next day, the car started up fine. I went to see if the car
  was driveble in order to bring it to my house to diagnose it. The
  car shook, there was a nasty vibration from the engine (at idle),
  giving it partial throttle (still in Park) made the engine rev
  smoothly.
• Inspected the spark plugs, and they were black and smelled like motor oil (see picture)
• One of the tires was flat, so one of the neighbours offered a
  can of puncture sealant, he put it in and then I drove the car back and forth to spread the sealant around inside the tire. The engine sometimes ran rough, and sometimes it “cleared up” and ran nice (good torque).
• The car was driven to my place and I removed the spark plugs to do a compression check, lo and behold, the spark plugs are a normal tan colour.

Tests Done

• compression was even on all cylinders (175-185 psi)

• did a resistance check on the fuel injectors, they were all 40-80 Ohms.

• did a resistance check on cables and coils, they are within spec

• check engine light was blinking (that can’t be good), codes read were “random misfire” and “warmup catalyst efficiency below threashold”. Codes were cleared, light did not come back on during a brief drive.

Question

What causes an intermittent misfire that coats the plugs with oil but then clears itself?

Update #1

Put everything back together intending to go for a test drive, but the engine misfired massively on startup. I shut it down and took the plugs out, and here they are.

Plugs #1 and #4 (extreme left and extreme right) smelled like gas, and they are both fired from the same coil (#2 and #3 are on a separate coil). Although the coil passed the resistance tests, I do find that the lead seems too short to actually reach the plug (#4 sits right under the coil without an actual spark plug cable). I suspect that running like this may have damaged the coil. Thoughts?

Update #2
I needed to get the car out of the garage to put winter tires on my daily driver (surprise! snow outside!). I reassembled everything, started this car up, it misfired massively and stalled. Twice. The third time, I revved it while in park, and the misfire cleared. I drove the vehicle to a nearby parts store (the car drove fine, good power) to get the codes read, it’s the same 2 again: random misfire and warmup catalyst efficiency below threshold. So, what causes a misfire but disappears when you rev the engine briefly.

Update #3
I had rented a fuel pressure tester, but this Mazda’s fuel lines don’t play well with others and I couldn’t get a good seal. I needed a break from staring at this thing, so I put it back together and drove it around the block to park it out front. The battery light comes on occasionally at low(ish) rpms, and clears if you rev it high enough for long enough. Do I have a charging problem? Or a voltage problem?