The situation you describe makes me think that the black marks are caused by exhaust air from the natural gas heaters. You don't say how old they are, and I am not familiar with the type of heater you are describing, but black marks are typically either from soot from the exhaust (from a cracked heat exchanger in your case...) or from too much heat over time "cooking" the walls, which doesn't make sense given the "black" marks you describe as opposed to a gradual browning.
Do you have a carbon monoxide detector? Any home with a combustable heat source like natural gas for either the furnace, baseboard heat, or water heater should also have a carbon monoxide detector. Invest the $40 in one, and instead of just installing it, try setting it near each of your heaters and see if it goes off.
I suspect you may be due for a visit from your HVAC contractor.