Blowing exhaust gasses into the cooling system

Blown head gasket cracked head or block are the only ways exhaust can get into the cooling system. Have seen more than one that would leak out but not into the cylinder because of the low pressure in the cooling system. Easy way to verify. Lock each cylinder at TDC and put 120-150 psi of air into the plug hole and watch the coolant for bubbles.

The EGR comes out of the manifold, up a metal tube to the EGR valve and through another metal tube into the front of the lower intake under the supercharger. Then up a short tube into the supercharger.
To test the theory you could remove the EGR valve. Apply air pressure to the tube that goes to the intake and watch for bubbles in the coolant.

One area that is an issue are the o-rings from the charger to the intake. You could be seeing exhaust being pushed through the charger and into the water jacket if one of those failed.
Not sure how you would test that without just pulling the charger off and resealing the lower and upper intakes.

I would try the air into the plugs then. If you get nothing there then I would probably replace the LIM and seals. I have head of the LIM having porosity but never had one myself. Then pressure test it and see what you get.