Have the provided flue terminate at a 12" deep drywall box on the ceiling. Paint the box the same color as the ceiling. You'll soon get past noticing it because it will be waaaay up there^^^ next to the ceiling.

Or visit a metal fabricator. He'll likely be able to come up something acceptable for way less than the $1k it will cost to buy the extension.

This is a current new-build; we expect to move in next week. For now we're going to live with it (wife's decision) instead of rushing to buy the $1k solution for an extra 12". I believe one of my trades mentioned they've had other clients have metal fabricators create extensions. At this point we have a lot on our plate so we can look into that and take our time. I'm just a bit miffed that the hood was already $3k and another $1k for a 12" extension puts it close to the price territory of a nice in-wall appliance. Overall $1k doesn't affect the overall home cost but as most of you know it's getting continuously pinged like this that raises the frustration. I appreciate everyone's input and it anyone has similar experiences they can share I'd like to hear them.

By the time you get a fabricator to rededign what the manufacturer has already designed, and you pay the custom one off fee, you won’t be far from 1K. 1K is kinda the bottom line custom piece price when you drive a BMW down to the hood. If you have a 98 beater GMC truck, you might get that down to about $600. Plus you have to take the time for several trips to the hood to approve the design and pick it up. Removing and reinstalling the hood assembly is on top of that. DIY. Standing on your island. Because you probably don’t have proper scaffolding boards.

Buy the item designed for the job. Have the builder’s trades do it before closing. That way, he is responsible.

A hood 48” above the cooktop is pretty useless and the extensions do not cost anything like 1K at least where I live they run about 300.00 per foot.I certainly would find a 12” box on my ceiling the worst possible solution. An induction cooktop has a bit lower CFM requirement than gas bit you still need to capture steam and odors IMO this is the time to do it right

With induction you don't have the IAQ health risks that you do w/ gas combustion so your main concern is odors, steam and grease. So, it's kind of what you determine you can tolerate. FWIW, I really dislike the odors of meals past so good exhaust is important to me. Also, if you entertain then it s/b even more important as it's really unpleasant to walk in to someone's house and have to deal with bad smells. Smell also has a huge impact on how enjoyable food is which is why better restaurants spend a considerable sum on good exhaust and frost air.

Islands are more difficult due to various cross currents of air so an island needs a larger hood and greater CFM to achieve the same result as a range+hood against a wall.

A hood at 48" is far from useless and this or higher is what you see in commercial kitchens and higher end residential. However, the higher the hood from the surface the larger it should be to be.

In the end it's what you can tolerate.

Kinda last minute to understand the hood will be 48" above cooking surface. Any coordination between builder and appliance consultants?

Your labor to undo and redo will be a few hundred plus the piece that makes it easy. Custom fabrication and undo/redo labor will exceed this.