A bad egr not matter what conditoin will cause the exhuast to be red.
Your o2 will malfuntion under extreme heat.
Too run that red you need to be running extremly lean, not enough fuel to air in the ratio.
Too bad you didn;t look at the rear exhaust pipes to see if they were red also it would clarify a few things.
Glad you mentinoed the hood trunk thing as i was confused as !Removed!