I have unmounted and disassembled garbage disposals a few times in order to get them unstuck. It's not hard and doesn't take long. You should be able to open up the grinding chamber to get to whatever may be jamming it. I've had little pebbles and pieces of silverware get tightly jammed between the blades and the casing. Maybe check YouTube for a video if you need encouragement.

My understanding is that the 6" studs are to provide the proper space for the required insulation. I've worked on plenty of load-bearing walls built from 2x4s before they updated the insulation requirements in the building codes.