Another option would be a case (such as a partial underwater housing) where the shutter release button is moved to the left hand side and connected via a cable to the remote shutter release terminal. You'd only have enough plastic to ergonomically mount the shutter button and gears, knobs and levers to access the buttons on the right hand side. Building this around a simpler DSLR would simplify the design.
Before I retired, I was asked if I knew where I could find a left handed phone...
Being right handed, you don't really appreciate the number of things designed for right handed use.
Drive in Australia and you can change gears in your Corolla with your left hand.
I understand the historical reasons, but I never saw the point of LHD cars. Wouldn't it be safer for most people to hold onto the steering wheel with their right hand and change gears with their left hand? But I suspect this follows a lot of comments from the left handers - you get used to using the equipment you have. (And, in totally unrelated news, I picked up a 1997 NA MX5 last week.)