[KittenClaws]

Your problem might be solved with a mini-split A/C-Heating System. It's great for room additions that do not have attic space to run duct work through.

We have one in our sunroom and it works like a charm!

The compressor unit sits outside and the unit is attached to the wall near or at ceiling height.

[LSAggie]

Don’t know if they would work in the poster’s situation, but I agree that mini-splits are the best! We had them installed in our 100+ year old house instead of the mess of running ductwork for central air. With four units we can “zone” the house, keeping higher temps where we aren’t, and lowering the temperatures in rooms we’re in.