It also doesn't look as though the cabinet underneath your cooktop is deep enough to house separate downdraft and cooktop units. Downdrafts are like 70's shag carpet. Everyone thought that it was cool at the time, but after a few years, everyone couldn't wait to get rid of them because of how awful they were at keeping your house dirty. In your case, there's an extra sin that needs to be fixed. There isn't enough room to pass by the cooktop safely, and no real room to prep on the island. It wouldn't pass a code inspection in a new build that way. If you go to sell, any buyer will want thousands off to be able to correct the issue, or it could be a complete dealbreaker to selling at all. You might as well spend those thousands now and enjoy a better functioning kitchen until it comes time to move.

If you can't repair/replace your vent motor(?), the next cheapest solution may be to get a new model Jenn Air cooktop, including a downdraft vent. I believe Jenn Air still makes these. One difficulty with other downdraft vents is that they are placed just outside the perimeter of the cooktop, rather than within the cooktop (as in your photo). A vent's efficiency deteriorates sharply the farther away suction is from the effluent source, so vents set beside a cooktop tend to work best for the one or two hobs closest to them. The best solution may be a vent that sits directly above the cooktop, but obviously this is more expensive. Moving the cooktop to an exterior wall adds other expenses, but may simplify exhausting the vapors. In general, venting from a corner (or a wall) works better than from the middle of a room, as you have things now. Of course, what and how you cook, and your local ordinance regulation, may also influence your decisions here.

Smoke and steam rise. You're attempting to contravene the laws of physics by trying to suck it back down rather than just trying to capture it and duct it to the exterior. That comes at a price of a louder fan and less effective ventilation. It's worth it for some to maintain an open view, but for most people the 10% of the time that they actually are standing at a stove it works out to be a more functional and less expensive layout to get the cooktop off the island and onto a back wall. Then put your prep area on the island where you'll spend 70% of your time in the kitchen.

Not only should the hood sides overlap the range cooktop, (60 inches may do vs. 48 for the range), but similarly the front-to-back aperture distance must be sufficient to overlap the range cooktop. The VaH drawing shows 30 inches, perhaps enough, although it is unclear how much of that might be lip or controls. Assume none. With an entrance aperture of 30 x 60 or 12.5 sq. ft. under the hood, at 90 CFM per sq. ft. the actual flow should be 1100 CFM -- probably adequate even on an island -- so long as there are no significant cross drafts. However, a magic lung isn't magic. The most we can generously assume is that the hood hanging in the air can flow the rated 1100 CFM. What it can do with some length of ducting, a roof cap, and a make-up air system imperfectly attempting to make the interior air pressure to outside air pressure equal is not knowable without analysis. I would go for a higher flow rate, ca. 1700 CFM. With care and expense, maybe 1500 would scrape by, particularly at 30-inches height, where the hood may block the view of taller cooks. A side view stick figure mock-up is recommended. Also, I am unclear how effective the entire entry aperture is, without more detail about how the incoming air meets the blowers and how the blower structure interacts with it. Pro style baffle type hoods are, in their way, somewhat less complex internally if the blower is moved to the roof where it belongs.