My immediate thoughts:

• Because the cooking zone is at the edge of the "apparent main drag," I think an otherwise obtrusive hood will look OK. It becomes part of the kitchen boundary. The kitchen forum mavens may have other opinions.
• Functionally, because your cooking zone can potentially cause cooking odor and grease to drift into the entire open space, a hood with good overlap and appropriate flow rate will be important. Downdrafts cannot capture and contain serious cooking plumes. Look at Wolf's design guide for examples of Pro Island Hoods of various sizes. Other manufacturers build or can build suitable hoods.
• When you specify the selected hood's characteristics, we can comment on flow rate requirements.
• You will need to start determining the architecture of your make-up air system, including where the air is taken from, where and how it is dumped into the house, and the interconnecting ducting, which may have to include heating, filtering, and a blower roughly similar to that supporting the hood.

The first image is of Wolf's longest Pro Island Hood at the boundary of a messy kitchen and a somewhat overtaken living room. The bi-level peninsula includes a 36-inch induction cooktop and an induction wok hob (not visible from the camera's POV); hence the extra long hood.

The second image is a view looking up into the hood. I don't think I've ever seen this view in Wolf's literature.

P.S. While normal suggestion is a hood 6-inches wider than the cooktop, with the longitudinal direction of the hood parallel to a long hallway in which there may be drafts, even from moving people, and because raising the hood base closer to 36 inches than 30 inches will improve visibility into and out of the kitchen space, I would recommend a longer than X + 6 inches hood length for your case. But unless you replace the existing cooktop with an X = 48-inch unit, you won't need a hood as long as mine shown above. X + 12 inches should be enough for modest drafts at 36 inches base height.

I also suggest that the front to back depth be as large as practical. The Pro Island hood above's entrance aperture depth is 26-inches inside dimension.

Kaseki thank you for that thoughtful and detailed response. In the last 24 hrs we have switched gears and are targeting a different house. This other one would not support a hood above the island. It will have the hood on an interior wall with ducting out the nearby exterior wall. Exactly how I do that ... remains to be seen. When we get a contract on the house (or a different one) I will repost and ask for more advice. Thanks

Assuming it is necessary to buy a house with a second floor, it would be helpful if the hood location on the first floor was aligned with a closet on the second floor so a duct chase can be installed in the closet at a sacrifice in closet space. Else, a joist gap path to the outside is needed that provides enough room for the duct sectional area called for by the hood flow rate.

If the sectional area is marginal, then if an exterior blower is used it can be selected to operate with the desired flow rate at the increased pressure loss of the undersized duct.

Joists terminate on plates that one would have to take a significant section out of to get outside. Some architectural advice may be called for depending on the details.

"The devil is in the details, but so is salvation." Adm. Rickover