I don't know the specifics of what sets the time limit exceeded fault. I would guess that it is a general fault for a closing or opening operation taking too long to complete.
As for resetting the controller, disconnecting the battery for an extended period should work. But how long is long enough? I think you have to do what Gilly said and disconnect power at the soft top controller.
But hey. As long as you have fault code 29, I think your system is dead in the water and a reset won't gain you anything.
As for the tranny, hopefully someone will weigh-in with some advice. I have the 5-speed manual in my car and know nothing about the automatic.