Soot is a symptom rather than the original problem. It is a product of incomplete combustion, which means the furnace has not been burning properly for some time. When the furnace is operating right, it will not produce more than a smudge coating on the burner chamber, even after years of use. Removing accumulated soot may get it sort-of working again, but something else caused that soot problem to begin with.
One possibility that has not been explored yet is a bad gasket. Since there are two fans on one motor shaft, there is a gasket in the housing divider that isolates combustion air from circulation air. If that gasket gets damaged or out of place, air flows from one side to the other. Usually you can smell exhaust inside the RV when that happens, but maybe not always. These furnaces are extremely sensitive to the combustion air flow, both air in and exhaust out.
A crack or pinhole in the chamber remains a possibility. Any sign of soot on the outside anywhere? Or maybe a partially plugged gas valve (though that should be too lean rather than too rich).