DEBUNKED ! Cold start , stop , restart = No knock

The (high) miles, with protracted clogged EGR, the codes and the behaviour, all point to failing head gasket.

 

Catch can install and dump an reputable fuel system cleaner following the instruction.

 

Thank You for the reply, Mendel
Funny you should mention the head gasket.
I've already been down that road and performed a head gasket block test, a week or so ago and the the results did not show head leak, thank god!
Is there a more definitive way to test a head, combustion in the cooling system is a tell tale sign, no?
Update as of yesterday:
Engine shutter came back, CEL back again. Ran the code and showing a P0300 multiple cylinder misfire.
Before I start throwing parts at it, anything I can check, perform immediately?
Could bad injectors coils be a culprit?
Again, any thoughts/comments are greatly appreciated?
I actually love this little car and am hoping to get a few more miles out of her.

 

I believe the "block test" is the one that tests for exhaust gas in coolant.

I think a leak-down test is best for finding the greatest variety of failures. The engine is rotated to have a piston at TDC on the compression stroke, then that cylinder pressurized (via the spark plug hole) with a special dual valve set. Then judging from what the valves do, coupled with listening for leaking air at various point, they can figure out what If anything is leaking on the head gasket. With the various passageways relying on sealing from the head gasket, there's multiple ways it can fail. Most common seems to be coolant getting into the cylinders?

While the plugs are out a boroscope inspection can be done too, to look for coolant in cylinder, one cylinder looking unusually clean is a bad sign.