You'd have to research them more, but there are hood models that actually install flush to the ceiling. I'm guessing they won't be cheap, but this might be a place to splurge given the location of your cooktop. Alternatively, Wolf and Thermador make a pop-up downdraft vent, too. I've done a pop-up downdraft vent for one of my remodels and they work great. See examples:

That’s ballpark low for a decent island hood. Island cookinn is the most expensive choice that you can make. And it’s the station that receives the least amount of time spent at it. Your prep station will have more time spent there. And unless your island is at least 8’, That prep station isn’t going to be on that island facing out. You would come in less expensive if you moved the cooking zone and made the island your prep zone.

Thanks, I am pretty committed to the island rangetop location and the vent out the ceiling due to physical constraints. The island is 12.5’ by 45”. Prep and cooking will be done on island.

Then pony up the funds to make your choice happen correctly.