I've had the CPS do everything you describe, but it usually didn't happen until the CPS heated up. A series of incidences, was when I'd drive my son to work every morning, five miles out five miles back, the engine would start really acting up at 9 1/2 miles. Some mornings at the same intersection a half mile form home. I initially thought it was a MAP issue because of the excess fuel/rich running condition.
But most of my CPS issues was re-starting a warm/hot motor.
Really rich on a cold motor was a leak in my MAP vacuum tube and/or a bad contact on the MAP connector. I found both when I was trouble shooting, don't really know which was the main cause, I fixed both at the same time.
Heard of this happening with a faulty sync sensor, injectors batch firing instead of sequence firing. Never happened to me. The motor wouldn't run right until the intake heated up.
I have had some cross fire issues, ignored my plugs so long the gap spread, carbon dust in the distributor cap from a worn rotor contact, spark would jump from pole to pole inside the distributor cap. I eventually notched the scorch marks in the inside of the cap. Spark would occasionally jump from plug wire to plug wire or find a path around the cable boot. I always assumed it was a resistance issue (high) because of the worn electrodes and high resistance in the plugs. Once the spark scorches a path around the spark plug it will continue to occasionally follow that path. Brake cleaner and a clean rag will usually remove the scorch path carbon.
Kind of reminds me of when my O2 sensor wire cooked on the exhaust, the insulation melted inside the foil shield and I was getting a short between wires and/or the shield foil. Bucking, miss firing got worse when the motor heated up, best guess is I wouldn't notice (or it wouldn't get bad) until the motor started transitioning from open to closed loop
