Ignition timing or idle speed would not be the cause of a Cylinder 4 misfire.
What should be done is to remove the spark plugs and run a compression test on all cylinders as a first step to make sure there are no engine mechanical faults. The readings should all be close to each other and considering the mileage on the vehicle, and assuming the engine is in good condition, you should see around 170 PSI on each cylinder.
The spark plugs should be replaced if pressures are good and the spark plug contact surface inside the coil boots should be inspected for corrosion, etc.
You should avoid the shop that recommended replacing all of the coils. An expensive shotgun wild guess at a problem without even verifying there are no mechanical faults first is not a smart move.