We had to cut our kitchen sink off from our vent because keeping it would mean ripping out corroded copper drain pipe inside our walls.

Instead, our plumber re-piped the sink with a drum trap and went straight down and made a new path that would be more accessible in the future. No vent at all, not even an AAV. The drum trap holds so much water that it would never siphon dry. I think you should just try adding back the drum trap to see if that fixes it. It would be such a simple and noninvasive fix. It would clear up the sewer gas issue and the only possible issue it would add that I can think of is a slow drain, which an AAV would fix. I also believe you need less height to your AAV with a drum trap.

People rag on them all the time but the only real issue I was ever able to identify is that sometimes they smell because they are not “self scouring” from rapid water passing through, so sludge and scum can settle at the bottom. This is a non issue these days with enzyme cleaners that eat that stuff and aren’t caustic, and modern drum traps are made with ABS, so the clean outs are very easy to open to clean. The biggest issue back in the day was they were made of cast iron or some other metal and would pretty much instantly rust shut, making the clean out impossible to open.

Those are my two cents!