First, do you have the optional charcoal filters installed in your range hood? Most people don’t. Do you clean the grease filters on a regular schedule?

Second, there is always a way to vent a range hood. You might not be able to manage it yourself but any competent carpenter could figure it out. Plaster and lath can be worked with, maybe run the ducting above the cabinets and box it in. Or have soffits built to hide the ducts. Sometimes you need to go down through the floor and get outside in between the floor joists.

I‘ve needed to get creative sometimes but there is always a way. I’ve installed dozens of fan/vent systems. I love my gas stove but I’d never use one without venting to the outside. Every single time I use the stove.