Could it be that the buildup actually changes that ratio....say 90/10 such that more air is being pulled down through the cooling tray when the damper is "dirty"?
That's what my thoughts are too, but we clean the damper every week. This issue is happens when we take the exhaust system apart and scrape from every pipe on towards the afterburner. The air flow damper is always kept very clean.
Too big of an exhaust pipe can create back-pressure, interestingly enough.
Too small, and it's too restrictive. There is an ideal range of diameters for exhaust ducting keeping maximum airflow efficiency in mind.
It's also possible that there are air flow leaks that are sealed with the bits collected in the first couple of weeks.
Just a couple of thoughts that remind me of my days on car forums.