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.

We recently did an update of our kitchen; painted cabinets, installed hardwood, new counters. We replaced our 84 Jenn-Air coil downdraft with a Bosch induction cooktop with a Bosch pop up. More expensive than electric, more expensive than a combo unit, but am happy with it.

We do not grill inside or eat fried foods so this works well for us. Some insist on an overhead vent, but for us that would have meant new ceilings in the main level of the house as we have popcorn that ties all the rooms together. We can't afford a major overhaul.

I think you will find you will need to replace the countertop; that Jenn-Air has different dimensions than current cooktops unless you go with a new Jenn-Air coil.

In my previous home we replaced a JennAir with a Thermador telescope vent and it was big improvement over the JA. It worked perfectly on the back burners, I found if I tilted a pan lid on the front burners it directed steam etc to the vent. If you go this route, get the tallest with a good size motor.

Looking at your picture I see if you have the depth a telescope vent would also make the cooktop safer. It would block anyone on the back side of the island.

We recently went through the same thing.

We went with induction cooktop and telescoping downdraft. Your island looks deep enough to handle the separate telescoping downdraft. With telescoping downdraft, you will lose storage space in the island. Only you can decide how much of that space you can give up, and whether the telescoping downdraft is worth it.

If you choose to investigate a downdraft vent, have the appliance store's installer take a look at it, to make sure your existing island can accept a downdraft.

In addition, our separate downdraft required a separate circuit breaker, its own electrical outlet, the blower (separate from the motor). The costs add up.

The least expensive and simplest option is to replace with a new version of the Jenn-Air (or clone) unit.

The Ceran Jenn Air cooktops available perform more inefficiently and are 10x more difficult to clean than induction. They are a step down from coil.
They don't yet have an induction top with downdraft.

We've had our Dacor gas cooktop and pop up vent for 6 years and we do love it. Yes an overhead vent is more efficient but it's not necessary for everyone - we do stir fry and often heat a cast iron skillet to sear steaks, we also cook fish in a skillet.

We have a remote blower motor mounted outside the house and our duct run is fairly short with only one 90 degree angle.

We've had a Thermador cooktop with pop up downdraft on a penninsula for over 25 years. Lots of grilling, stir frying, and a sauteing. It works reasonably well, and I believe the new Thermador pop up projects even higher above the cook top. Now having said that, we will be going to a range with hood on our upcoming reno...

We just had a new Jennaire pop up downdraft (36) installed in our 22 year old house replacing the original Jennaire and the mechanism & vent pipes take up the whole cabinet underneath. We are very disappointed that no one could tell us that in advance. I need that cabinet.