When we opened up the ceiling, we found the power lines were all just draped over the drop ceiling, the stove wall was built out with 2x3's and the ductwork for the next room was hanging below the rafters.
You can see that we used straps of metal to pull the ductwork up. The ductwork couldn't be pulled all the way up, so we built up the joists with scrap wood to secure the drywall. So, technically, my drywall dips down there, but you can't tell by looking at it.
The vent into the kitchen was a huge box that had to be cut down to fit the new ceiling height. Here's the final product.
I did that with a hacksaw and a pair of tin snips.