I'm bumping this up in hopes of getting some responses.

It sounds like you already made up your mind.

Actually no, we are still evaluating a vented hood option, but in case that is not feasible/economically viable we are trying to assess the relative merits of downdraft versus a recirculating hood. So, still looking for input on these options.

You need to figure out exactly what you can do for venting before choosing your stove - a recirculating hood is not going to be at all adequate for the performance of many of the models of rangetop by the brands you’re mentioning, and even a high quality downdraft is going to limit that list.

You want unobtanium. You can’t contravene the laws of physics. Asphyxiate, or buy something consumer grade for cooking.

Sophie is correct, if a bit harsh. Serious cooking and in general gas cooking leads to significant uprising cooking plume velocities (up to 4 ft/s). Less with induction. Each plume expands as it rises. Ideally, each plume is overlapped by the hood entry aperture (capture) and pulled past a filter into a space (containment) from which it is expelled outside.

A recirculating hood with an extensive filter pack can also perform this task, at least in principle, but may also be as expensive as an externally exhausting hood. It will negate the need for a separate make-up air system, but in my view should only be used with CO detectors. Humidity could be a problem.

The Vent-a-Hood ARS system is the only one that has been reported on here by a user. He considered it adequate in removing smoke and grease, as I recall.
https://www.ventahood.com/index.php/about/innovation/ars

The flow rate would have to be compared with what would be required for good capture. I haven't investigated what they provide. One hopes that VaH has selected a blower that can handle the necessary flow rate in the presence of so much filtering.

Pop-up, down-drafts, etc., violate the capture principle, attempting to pull air sideways and into a vent where it is forced to move against its initial velocity vector. A rear pop-up's capture from front burners is likely nil, and at the front side of the rear burners there will be missed plume. Some configurations will disturb the gas jets. Demos with hot steam or smoke candles are not adequate examples of functionality. Either use peanut oil at the smoke point from hot pans, or schlieren photography with pans at the smoke-point temperature to determine capture capability.

You mentioned the second time that you are evaluating a vented option. In your first post you mentioned it may be cost prohibitive or structurally infeasible. If you can share some details on why that is, you'll get more useful responses aside from the harping to go vented.

kaseki, thanks for the detailed response, much appreciated. A vented hood is not impossible, but may require pretty extensive work in the ceiling (this is not a full kitchen remodel, just a refresh with painted cabinets, new countertops, a new island configuration, and new appliances). This is for a second home and I need to check to see which way the ceiling beams run when we are there next weekend. If they run sideways to the front of the house, then it will be less work to take the vent to the ceiling and out to the side of the house (still requiring tearing out drywall and hoping there is no obstruction such as ductwork or water pipes that are currently hidden). If the ceiling beams run lengthwise, then it becomes nearly impossible unless we tunnel through the beams to take the vent to the side of the house. Running the vent to the front or back of the house is not an option (intervening rooms in both directions). I completely understand the physics of why a downdraft is not going to work well.

It's pretty well established that the physics of downdraft simply don't support effective venting. And recirculating hoods are ineffective, even for electric, as my stay in a ski condo last week will confirm. A weak residential coil electric + dual screen overhead non-venting hood + 11 hamburgers and an open window = a condo that still smelled like hamburgers three days later.

However, when I was looking at the VAH site the other day, I bumped into the Vent-A-Hood® Air Recovery System (ARS) Technology. Does anyone have any clue if this is worthwhile to folks in an external vent bind?

https://www.ventahood.com/index.php/about/innovation/ars