The furnace combustion chamber is not accessible to normal cleaning , just the intake and exhaust tubes.
JMHO : remove the furnace and strip the blower assembly and the burner from the combustion chamber , and flush the chamber with water ; you'll probably be surprised at what you'll get out .
I've done this when helping a friend , the mud daubers got right inside and we got 5/6 lbs of mud out , cured his short cycle issue .
I'm thinking you're issue will be small fried rodent .
It's not a hard job , just time consuming , take pictures as you go and have an old egg carton handy to keep screws organized.
The yellow box in the photo shows the combustion chamber , it zigzags through two layers after the burner ( silver plate ) before the exhaust . This is a Suburban , but your Atwood will be similar. If you don't have a manual they are usually on the manufacturers web site as a free pdf download.