I am relatively new to sliders so I think I will defer to others.
But, I do know a bit about RV furnaces. There are two initial causes of soot from the furnace that I would look into before taking it to a RV shop for expensive repairs.
First, the orifice and burner tube needs to be looked at and cleaned. Any obstruction in the tube alters the air/fuel mix and can produce soot. There are some insects that just love the propane and/or the captene in it so they will nest there when they can.
Second, the combustion chamber should be inspected and cleaned. Repair shops use a long cleaning tool that resembles a brush for cleaning test tubes but bigger. I've used my shop vac by removing the plastic end and just shoving the flex hose into the chamber and stack. Some feather dusters or similar can be adapted to work. I can even envision a swiffer duster being modified to work.
BTW, the above generally applies to the fridge and water heater, too.
Looking at Suburban's website, they don't offer manuals unlike Atwood or Dometic. Every FAQ they have there wants you to go to your dealer or a qualified RV tech for any service at all.
http://www.rvcomfort.com/suburban/
I know I'd be getting my tools out and taking a look-see for my self before dragging my trailer back to the dealer and paying money for them to look at it, but that is a decision you'll have to make.