Many years of dealing with home maintenance projects has taught me a lot.
To avoid paying to cool the whole house, we put window units in each bedroom (and computer room). If possible, we use the window unit instead of the central air.
Upstairs rooms are very difficult to cool by nature. Cool air is denser than hot, which makes it heavier. It takes a lot of pressure to make cool air go up. Without the vents, it is the same as impossible to cool second-floor rooms.
Furthemore, the doors should be kept closed with no leaks at the bottom. Any cool air that might get into your room will collect close to the floor, and escape through the opening at the bottom of the door.
Have you considered putting a window unit in your bedroom?
It would be cheaper than paying someone to run sheet metal.
Chuck