Well, a cylinder will fire correctly provided it has 1. spark, 2. at the right time, 3. compression, 4. fuel and air of the correct mixture, and 5. a way to rid the spent exhaust gasses from the cylinder.
So it seems you are on the right track. Has the shop visually verified you have a good spark at the spark plugs on 2 & 4? My first suspicion remains something wrong with the coil system. Are you certain when you moved the coil packs, that was done correctly? By this I mean, was this the first time the person who moved the coils around has done that job before?
If you weren’t getting a good spark on 2 & 4, that would explain a “rich” mixture symptom. The gas wouldn’t get burned, so it would come out the tailpipe.
Another idea, no gas is being injected on 2 & 4, so the other cylinder might get an extra dose of gas, producing a rich symptom. Have you verified the injectors on those cylinders are getting pulsed?
A faulty ECM, ECM connector, or igniter, grounding, or other wiring problem could cause this. Was any work done on this vehicle just prior to this starting?
A couple other random thoughts. Have the wires to the spark plugs been replaced? Try looking at the engine running in the dark, see if you notice any signs of visual sparks jumping around.