I'm an original owner of an 03 GT. Lived through several transmissions so far, and still going back for more. We just crossed into the 200,000 mile territory a few months ago. So I have some (LOL) experience with these issues.
Call it a damper door, call it anything, but it is annoying. The simplest, cheapest solution is to keep the button on RECIRC. For those of us too chicken and too cheap to do anything further, it solves the clicking noise issue in a flash. Your car will reset it to flow-through when you turn on the defroster, so just remember that you need to put it back to recirc when you're able to see.
Crunchy/touchy transmission. We learned long ago that it's a total stop or life is not good. It's a quirk the car has, which isn't necessarily a bad thing. A little inconvenient perhaps, but I'm looking forward to getting my car up past the 300,000 mile mark. And you know, the Yamaha engine in the GT will probably get us there. I'll probably be looking at another transmission (or two), but with my handy, dedicated mechanic who works wonders and tells me the smart, cheap fixes (instead of the $500+ to change a little Toyota part that clicks), we'll get there... Enjoy the ride!