I have the same set up. Hot air rises! Ductwork is not going to help. I have a window A/C in my space. It is in the adjoining room but it works for me. I bought a new one last summer. It has a remote control....who knew?! You do need to make sure that the BTU's support the size of the area.
When outside temps get up there later in the summer, i put a small fan in front of the air conditioner to help push the cool air into the next room.
Hopefully I will be moving my sewing room into the next room if my DH puts his hobby in the newly waterproofed basement!
Sandy.