Many years ago in my past life as an auto mechanic, popping in the intake meant lean and popping in the exhaust meant rich. This is/was typical for engines when the carburetor mixture was way off spec (note that there are a lot of other things that can cause popping). For popping out of the exhaust as you described, there needs to be unburned fuel entering the exhaust.
How is the compression? I know that if the dealership scoped the vehicle, they should have picked up a compression problem while monitoring the cranking amps. Perhaps one of the folks that is more up to speed than me might be able to correct my memory if the following statement is wrong. Measuring cranking amperage to determine the relative cranking compression can sometimes miss a head gasket failure between cylinders.
I would start with a compression check with all the plugs out and/or a leak down check. It sounds like someone has been replacing parts like mad trying to correct the problem and I assume that there is no way to mix up the coil wiring on your engine.
Next I would ensure that the valve train is in good shape: (1) no rounded lobes on the cam (2) no broken or weak valve springs (3) no lifters that are not bleeding down properly.
Tiny, are you positive your engine is in good mechanical condition? If the engine is mechanically sound, then start looking for some condition that would allow unburned fuel into the exhaust
