You really can't do this, functionally. I am pretty open to alternatives to the conventional on-the-perimeter-with-full-hood option, but if you are going to do a system flush with the ceiling, you might as well install a system designed for it and get some function out of it, or not do it at all.

If you install something for cooktop ventilation it will have to be accessible and have accessible removable grease filters. What you are describing might give some room ventilation, but the works still need to be accessible. This system, by Sirius is 60" x 40" x 7" thick. With attic above it could be mounted fully flush which is higher than recommended (I think 84" above the floor is what it's designed for).

If you don't do something like this, and you end up doing some sort of fan for room ventilation I would actually avoid mounting it over the cooktop to avoid getting grease in the ducting. Mount some sort of linear ventilation in the ceiling but away from over the cooktop. Not every locale requires exterior venting for cooking so you might be able to get away with it where you live.

Thank you for your suggestions. Yes, your photo is very similar to the Best model, 34e6sb, by cirrus, that is meant to mount flush into a 7 to 9 foot ceiling. Measures 43x27 inches. Really beautiful. I would install it if it wasn't for my budget constraints. After living with the ineffective or broken downdraft, I am determined to improve my ventilation in the room. I like your idea of not putting it over the cooktop. I never thought of that. I could pick an unobtrusive location for the intake, and then plan to clean it as needed.

Has anyone done this? Would I just use a standard whole house fan with remote blower venting through attic to the exterior.

The Best Cirrus fans are $1800-2200, so I would really try to find whatever the difference is between the ~$2000 and whatever the cost of the components are for what you're thinking of and come up with it somehow even if it meant downgrading something else a bit.

I doubt the difference is going to be more than a few hundred dollars.

You could spend a couple hundred on the linear ventilation grille for the ceiling alone.

I do love the way they look. But I believe that the cirrus units do not include any fan at all, they are simply the grill and light system to mount on ceiling above cooktop. Consumer would install into ceiling and buy separate blower and ducting. Correct me if I am wrong.

You are correct, the blower is at least another $400.

Not a whole house fan! They are very powerful - too powerful. You wouldn't be able to use it without all the windows open, and it would suck from all of them. And very, very noisy. I have one in a hallway. It's great for certain times of year but definitely not for kitchen ventilation. A wall exhaust fan - my home originally had one by Broan. I put in a JA across the room so the fan was walled off. I looked in to getting a similar one for the reconfiguration I'm working on. I really dislike vent hoods. However, the wall exhaust fans are almost the same as 50 years ago. Not powerful enough, incredibly noisy, and still mostly made by Broan. I was also cautioned that sucking grease into the exposed motor would eventually ruin the motor.

I still have not made up my mind what to do. Several months ago while internet searching I came across a company that designed home kitchen exhaust systems. Sorry I did not book mark. It did not read to be out of line from "prebuilt" vent hoods but you would have to figure out and provide whatever in-kitchen exterior thing you wanted to look at.