Hi, folks. I could use some advice about finishing my laundry room.

First, I live in a really old house, which was renovated in the late
90s. The did a terrible job on the utility room. There are a number of
issues that I'm resolving this summer, but the one that I fear the
most is fixing the ceiling.

Here's what they did. First, it looks like they tore down the old
plaster ceiling, but left the lath and all the crap that comes with
it. Then, they hung air ducts all over the place. finally, they put up
a drywall ceiling *around* the ducts. The ceiling is still above the
ducts, but the area above them is exposed lath. The problem with this
is that 120 years worth of dust and crap constantly sifts through when
the people upstairs walk around. So, our laundry room is always dusty.

I was wondering if anyone had any clever ideas about how to remedy
this situation. I would prefer NOT to remove any duct work. I thought
about using partial sheets of drywall to slide above the ducts, but it
would be almost impossible to screw them into anything that might
support the weight. I also thought about installing a drop ceiling or
enclosing the ducts in drywall, but access to the joists is limited.

Short of hanging a tarp, any thoughts?

Thanks!
Joseph