Should it possible to remove the heat exchanger from my natural gas furnace?
Firefox, firebox who cares (it's just a typo). But why would you take the furnace apart to clean the evaporator coil. Does it really need to be cleaned. If really needs to be cleaned, there are service companies in business to do this type of work and to protect people from themselves. I and many others on this site have worked on furnaces and A/C units for many years and I don't think any of them have ever taken a furnace apart to clean an evaporator coil.  Please  call a licensed furnace service company to correct the  mistakes you are making and save your family from a pending disaster. If you do not know what you are doing PLEASE PLEASE call for help.