James,
I hate to say this but, as you already know, you've got a real problem!
If memory serves then the rod travels diagonally from the front right of the heater unit to the rear left, where it slots into a cam that transfers the forward backward movement of the rod into rotational movement of a further rod, this 2nd rod rises from the rear left bottom of the heater unit to the top left where the rotational force operates the flaps!
In a Uk car, by emulating the stetchy guy from the Fantastic Four, it is possible to access the screw that holds the cam on to this 2nd rod, slacken it off and release it, which allows enough play to refit the 1st rod and the replace the cam and Bingo job done! In your US car I fear that even were you blessed with the phyisicality of a squid you're not going to manage that!!!
So I fear that you may need to turn your mind to the notion of removing the entire dashboard to gain access. If you decide that this is the only way and need some help then shout, mines been in and out more times than the, er, hokey cokey!!!
Pete
