Spray foam insulation is great for fully insulating tight spaces, then you could spray paint it matte black. If the visual texture isn't to your liking, you could spread black sheets along the ceiling and fasten the material into the foam with purpose made large wide thread screws.

All that said, it'd be a lot cheaper and easier to go with rigid foam boards that are snug-fit into place. It's not as good for sound insulation, but it'll look better and be easier to finish if you don't like the texture of the black painted expanded spray foam.

Would suggest adding furring to your floor structure and installing a gypsum board ceiling.

Spray or rigid foam, because it is a fire hazard, cannot be left exposed without a gypsum board or plywood cover.

To retain an "exposed" ceiling look and some extra height between joists, you would have to fill between the joists - of which you have a few realistic choices and methods. But, because of the C channel joist shapes and shorter height, building up enough mass to make a discernable difference worth the trouble, would at the same time not be worth the trouble.