I would not worry about the 2cycle oil. I use it for lubricity with no ill effects. It works better than the other products mentioned. You just want to make sure it contains no ash.
I would pull the EGR first to make sure its not sticking and give it a good cleaning before you replace it. Otherwise I would suspect an EGR cooler failure but this would be unrelated to the 2 cycle oil.
Easy on the flames folks. We all make different decisions. While some of us would not choose the same decision as others we are still here to help each other out.