We need a lot more information, I think.

Ideally, I would suggest, rip out your central AC system and replace it with a minisplit heatpump. Takes up less space, much more responsive, much more energy efficient, and neatly solves your problem. Unfortunately, it does incur a big upfront cost. So, this might not be what you want to do.

The next question is, what is above your kitchen? Can you vent to the roof? If so, you might be able to have an S-shaped section of vent pipe that navigates past your AC ducts.

Or you might be able to push your AC ducts into the ceiling joists above, and then there are all sorts of other ways to either route the vent to the side of the house or past the AC duct.

If you can run the AC duct in the ceiling, that would also allow you to move it away from the wall. Of course, a bigger soffit would do the same job, but I can't tell whether that would look OK.

It might also be possible to place the stove somewhere else. Or, if you are really desperate, you could get a VentAHood recirculation system. It's not as good as a properly venting hood. But of all the recirculating hoods, this is the only one that actually does work, as it has extensive filtering built-in.

There are so many possibilities. But it is really hard to tell without seeing more details and without knowing your budget.

We can't see the whole AC plan, but I would want to consider whether I could add AC duct somewhere to duplicate the feed such that it connected to both sides of the room. Then I could cut the existing duct over the range and block both ends at that location.

Another option is the put the range on the outside wall and vent straight out below the soffit.

Kaseki thank you for your consideration. This is actually the least invasive way to run my AC ductwork, it’s not possible to feed it from two locations without compromising the pantry and powder room on the other side of the kitchen.
Above the kitchen there are bedrooms and bathrooms, so unfortunately venting up is not an option.
The duct and soffit are a full 12” below the ceiling because of the position of the joists. If I can get the hood duct to the ceiling in front of that duct then I would be able to run THAT duct between the joists and vent out on the window wall. That is do-able, if I cover the range hood with something decorative that comes out the depth of the base cabinet, however, the duct then runs through the top shelf of all my uppers on that wall. I’m trying to avoid that.
As far as kitchen layout goes, I’ve spent many months figuring out what works best for my lifestyle (I cook tons) and moving the range is not really an option.
I thought of putting an island chimney vent hood CLOSE to the wall above the range but the ones I’ve seen won’t clear the 12” AC duct..
I also saw a hood by futuro that looks like a large rectangular stainless box and it somehow floats on the wall. There’s no pipe or duct above it. Any idea how that unit vents out?

M I apologize I meant to also thank you in my previous post. I appreciate your time and suggestions..

No information on the Futuro.

Do you have a basement that could be used? One can go down within a wall and go out via a basement or crawl space. The blower will have to be sized for all the pressure losses, and this may require a blower in the hood and one outside or in-line, depending on factors not yet apparent.

Actually, we need to start with the cooktop size, the hood size, the required CFM, how MUA is introduced, etc., and then we can consider what duct sizes are appropriate and what blower rating is appropriate.

If you decide to vent down, make sure that is legal where you live. San Francisco building inspectors won't sign off on it. They're afraid it could trap grease in a low spot. And that's a fire risk

Wouldn't that also preclude using such pop-up down-draft units as the Broan Cattura. One would hope that some type of grease trap could be used, where required.

According to my HVAC guy, San Francisco inspectors only allow grease traps on commercial installations. I have no idea what that means for downdrafts that are intended to have grease trap by their very design. Don't shoot the messenger :-) It might just be one particularly strict building inspector. But that's what we have to deal with here.

I should add that the amount of grease that gets past baffle and mesh filters and isn't ejected to the outside in residential systems is generally slight -- sufficiently slight that for most installations it will only varnish the duct interiors over time. (By varnished I mean leaving a thin film of rancidized grease such that flammability is reduced due to oxidation.) I would not expect puddles of grease to form. Inspectors, of course, have to consider the worst case household cooking scenario, so may be more stringent than one might expect from experience with benign grease condensation conditions.