Farmhouse sinks, with the open front, can be retro-fitted into existing cabinetry in many cases, but will require some cabinetry work.
Given the depth requirement you would like and the available clearance under the sink, an under mount may not work but a flush mount may fit, or a top mount version that sits a little higher. A quick look shows that there is even a faux farmhouse sink that has an apron that fits over the existing cabinet base giving the illusion that it is cut into the cabinet. Have not seen it in stainless steel, however, only copper, but I didn't look too long.
Here's a pic
Here's the site link:
https://www.rachiele.com/retrofit-copper-apron-sinks.aspx
Do a bit more searching as there are literally hundreds of sink options available.