I would be looking at fitting a centrifugal fan with 4 inch outlet( recessed would look better) I assume that a 6 inch axel fan was there before did it bun out due to resistance of ducting ?. You need to find out where the ducting is exhausting to. It is no good ducting into the joist space between ground and 1st floor.This reminds me of my old boss on some 3 story houses telling the electrician to grip fill fan grills onto the outside walls by leaning out of the bathroom window instead of hiring tower.