Six inches isn't enough to be impactful or useful for over cabinet lighting, really. I'm with your husband.

I like the gap for some interest. Is it enough to continue crown molding from the rest of the room up there?

To the ceiling.

Becky Sikorsky: No, the tall version does not "just fill the space with stacked moldings". The cabinets are taller, by 3 inches, so the molding is not much larger.

A six-inch gap just looks like a mistake. It's way to small to be useful and will just be a dark, weird space on top of the cabinets. To the ceiling.

Is it an option you have the range hood to the ceiling and then put extra moldings to the ceiling on the other cabinets? Your husband gets his desire for everything to the ceiling, but you still get a range hood that stands out.

To the ceiling and IMO those staggered cabinet heights are the worst design feature ever in a kitchen

If the cabinets go to the ceiling, it creates a nice clean line. By varying the heights, not only does it look like a mistake, you will create gaps which are hard to clean.

If you want to add focus to the hood, wrap it in metal instead of wood. I agree with those who suggest that higher cabinets are better than larger gaps, and that staggered height adds nothing good.