I would for sure spend the money to remove the wall and I think the idea of a large island with stools is great if you have the space it is hard to tell from the pics a floor plan woulf be very helpful and maybe some more pics from different perspectives also.

Well, for lack of a better idea, since you find it a drafty little space. I'm assuming the draft comes in on the right? Most of the necessities in the area are located of the left side; i.e. vent, thermostat, light switch etc. What I would do I think is caulk up the drafty spots, maybe even add sized poster board wrapped in batting I covered in a gorgeous fuscia with diagonal grosgrain ribbons every which way covered with a heavy velvet to be attached to the area above & below the window. (Of course remove the drapes that are hanging in there). This for the purpose of using it as a pin-it board for notes. Attach a table height board covered in felt to carry across the full width of the little room. Leaving just enough space for a comfortable little antique desk chair. Paint the back wall a bright cobalt blue, paint the ceiling a silvery pearlescent white. Find a way to attach a clip-on task lamp. And stretch a heavy duty enough wire across the top of the opening and complete it with a heavy doubled velvet drape with a drooping valance. Place a swag with fringe & jewels on it to be closed when not in use. Voila intrigue is yours!

My downdraft is great with outside motor so not too noisy. Having said that I would also have been happy with a ceiling extractor if I had the space above for the venting.

You can not go past a Schweigen with externally mounted motor. Even on its highest level I can not hear mine above cook top cooking noises. The only disadvantage is remembering to turn it off. (I say that very tongue in cheek).