Not sure the procedure run down was really required, but nevertheless the answer is in there.
So at this point, we know
* you have what appears to be air movement at the entrance to the fan because you did the tissue square test.
* the room has the door open during the creation of the moist air from the shower so should be able to replace the air that it exhausts through the fan
We don't know for sure that the moist air is truly going outside through the roof vent, but that seems to be a different issue than moving enough air to counteract moist air build up.
To be determined:
* Is there something restricting maximum air flow between the fan and the roof vent exit. For example, kink in tubing or something restricting a damper at the fan exit or roof exit, or too long of a run to the vent exit
* Is the fan truly powerful enough
* Is the fan placed well within the bathroom ceiling relative to the shower
Other than that, I'm out of ideas. Hope someone else has some suggestions for you.--
nohup rm -fr /&