Just a tip to help.
Check if you have water or coolant in the oil, since oil systems work at higher pressure oil will be going from a higher pressurized side into the coolant which is at lower pressure, the top pressure for cooling system is 15 or 16 psi, oil runs at a higher pressure, this will indicate oil getting into the coolant at heat exchanger, the xkr has one under the supercharger in the v of the block, on the other hand the head gasket side will be different way since oil is just dripping from valve train down to the sump, water or coolant will be in the oil if head gasket is blown and coolant excaping (usually this happen with compression blowing from the pressurized cylinder 150 psi into the cooling 15 psi or oil drain back under atmospheric pressure at idle due to pcv vacum), when the engine is shut off hot pressure will remain in the coolant side and will try to go in the oil heat exchanger side with minimal possibilities because the oil in the galleries does not drain back and has minimal space to accept the coolant and if a little coolant gets in it will evaporate and be discarded by the pcv system when the engine gets hot again, base on the pressures explained here I would check the engine oil and if there is no emulsified traces of oil and coolant in the oil, then for sure I would look into the heat exchanger or engine oil coolers, check the one in the v of the block for a bad seals, on the other hand if a head gasket would be blown, when the hot engine is shot off, high pressure will not be in the cylinders anymore, this will permit low of coolant to the cylinder and could cause hydrolock when trying to crank it the next day after cool down, and definitely will get a burnt coolant smell in the exhaust. my 2 cents
