These issues with back firing on shut down, I think are about lean running EPA regulated engines. With the key turned off, there's no spark, and something glowing hot in the engine or exhaust is lighting the fuel which is still being pulled into the engine simply because it's still spinning. A fuel shut off soleniod could help, but there will still be a shot of fuel at first.. letting it idle and "cool" internally for a second before shut off might help. If the kohler carb has low end mixture adjustment it might be richened to help the acceleration stumble, and lower the temps in cylinder and exhaust. Lean mixtures make heat.
My 12 year old argo had all of these symtoms when new, some said it was glowing hot tips of welder wire feed protruding inside the muffler, etc. Since modifying my engine 3 years ago, different fuel and exhaust, it's never once back fired. Just some ideas..
To Invent, you need a good imagination and a pile of junk. (Thomas Edison)