Hard to really give the best advice without a sketch of what you're dealing with, but what about going through the stairwell behind. If it is a stair down is there enough headroom above to have a 4" pipe crossing. What's the possibility of extending the run in the crawl space? You don't want to have the run too long (code restricts it). Remember also, if you are running the exhaust in an un-conditioned space and you live in a climate that has freezing temps, then you should to insulate the pipe to minimize moisture condensation as this will grab onto the lint and eventually clog you line.