I would remove the light box and replace with pendants. Is the downdraft working for you? Decent hoods are expensive to install. I'm all about function so I am putting a lot of attention into the hood in my kitchen, but it depends on how you cook. Lovely space to work with :) .

Yikes! Is this a test question for wanna be interior designers, or a lesson in what not to do for architects? Just where does the downdraft system vent to, the infinite dirt filter below? Given a limitation on cabinet costs setting the scope of kitchen changes, conventional solutions that meet the standard requirements of effective cooking effluent plume capture and containment (C&C) are not apparent. Down-draft ventilation is far from optimal for C&C, although some find it adequate when the inlet is high enough to divert some of the rising and expanding plumes, given an adequate blower and duct system. A vertical duct should not be excluded until you do some exploratory work to determine the layout of bedrooms and their closets with respect to the kitchen layout below. Perhaps the seller has blueprints. A horizontal duct below your ceiling may not meet your sense of aesthetics. Embedding a duct in your ceiling may be feasible, albeit messy. Some of these approaches could make cabinet changes to get the range onto a wall space the lower cost option. You may be in a position where you have to adopt the solution that people in controlled city condos sometimes have to adopt -- a recirculating vent system that actually works. At one time, excluding commercial systems, a recirculating hood that works was an oxymoron. Some residential systems have appeared in recent years that have received positive comments here, including one from Vent-a-Hood, and maybe from Broan. Searching this site for 'recirculating hood' should provide some leads. I am not in a position to do cost estimating, and in any case believe that homing in on a few solutions trading effectiveness, aesthetics, and installation complexity need to be selected first. kas

The next question is, where would it have gone otherwise? If the builder ignored several obvious shorter routes for the crawlspace, maybe it is a questionable decision. But if it goes through the crawlspace to avoid blasting someone in the face on a deck or patio or to avoid a vaulted ceiling upstairs from the kitchen or some other convoluted path, maybe it is the better of several not great options? (My house has corner to corner glass on both front and back elevations on the first floor and a glass wall with exposed sheathing ceiling on the third floor. (And common wall houses on each side). There are very few places to run any ducts.We are fishing a vent duct straight up and through a knee wall that avoids any of the glass walls, but my neighbors have one duct that bumps out in front of one of these windows, and another vent that exits exhaust right next to their front door. Not attractive. We are able to run this duct relatively straight because we are demoing back to the masonry wall between houses.)

Any particular reason that you want to come off of the existing fan power, like maybe a switch in the island structure? I'm sure it's doable but probably easier to feed it from elsewhere. If you have an unfinished attic immediately above and an unfinished basement immediately below, it'll be simpler than otherwise. I recommend that you call in an electrician to get it evaluated. JM$.02W