I am renovating my 1st floor bathroom and am planning on installing a PANASONIC 110 CFM exhaust fan.

I can't cut holes in the joists above because there is plumbing in the way and the joists are only 8 inches and my exhaust fan has a 4 inch exhaust.

I have 3 options:

1) Lower my ceiling a bit, enough to run the 4 inch duct, but I really don't want to lower my ceiling just for the exhaust fan.

2) I need to rebuild a soffit where the bathroom wall meets the kitchen behind it, since there is a kitchen exhaust fan above my stove which vents through the shared wall and then out to the exterior. I can run an additional vent for my exhaust fan behind the soffit, but the ductwork would run 2 feet between the joists and then turn 90 degrees downward and then another 90 degrees in the direction of my exterior wall. Is that a problem??

3) screw the installation of the exhaust fan on my 1st floor bathroom and install it in my 2nd floor bathroom instead.

I like option 2, but i'm not sure if there's any problems associated with it.