I'm not super-experienced, so this may sound stupid.
I'm from the North-East, and when I go on a trip, it's almost always raining or wet. I think that keeping a tent soggy in a small bag is a bad idea, so I wipe it down with a small pack towel before I put the tent away. That being said, I haven't found a good way of wiping the tent floor without getting the other parts wet.
As well as a TT Notch, I have a GoLite SL-3. That guy has the advantage of a separate floor, so I first wipe down the tent, put that away, then wipe down the floor.
Maybe it just takes practice. What do you think?